In order to improve the performance of time difference of arrival(TDOA)localization,a nonlinear least squares algorithm is proposed in this paper.Firstly,based on the criterion of the minimized sum of square error of ...In order to improve the performance of time difference of arrival(TDOA)localization,a nonlinear least squares algorithm is proposed in this paper.Firstly,based on the criterion of the minimized sum of square error of time difference of arrival,the location estimation is expressed as an optimal problem of a non-linear programming.Then,an initial point is obtained using the semi-definite programming.And finally,the location is extracted from the local optimal solution acquired by Newton iterations.Simulation results show that when the number of anchor nodes is large,the performance of the proposed algorithm will be significantly better than that of semi-definite programming approach with the increase of measurement noise.展开更多
This paper considers Stokes and Newton iterations to solve stationary Navier- Stokes equations based on the finite element discretization. We obtain new sufficient conditions of stability and convergence for the two i...This paper considers Stokes and Newton iterations to solve stationary Navier- Stokes equations based on the finite element discretization. We obtain new sufficient conditions of stability and convergence for the two iterations. Specifically, when 0 〈 σ =N||f||-1/v2≤1/√2+1 , the Stokes iteration is stable and convergent, where N is defined in the paper. When 0 〈 σ ≤5/11, the Newton iteration is stable and convergent. This work gives a more accurate admissible range of data for stability and convergence of the two schemes, which improves the previous results. A numerical test is given to verify the theory.展开更多
Cement density monitoring plays a vital role in evaluating the quality of cementing projects,which is of great significance to the development of oil and gas.However,the presence of inhomogeneous cement distribution a...Cement density monitoring plays a vital role in evaluating the quality of cementing projects,which is of great significance to the development of oil and gas.However,the presence of inhomogeneous cement distribution and casing eccentricity in horizontal wells often complicates the accurate evaluation of cement azimuthal density.In this regard,this paper proposes an algorithm to calculate the cement azimuthal density in horizontal wells using a multi-detector gamma-ray detection system.The spatial dynamic response functions are simulated to obtain the influence of cement density on gamma-ray counts by the perturbation theory,and the contribution of cement density in six sectors to the gamma-ray recorded by different detectors is obtained by integrating the spatial dynamic response functions.Combined with the relationship between gamma-ray counts and cement density,a multi-parameter calculation equation system is established,and the regularized Newton iteration method is employed to invert casing eccentricity and cement azimuthal density.This approach ensures the stability of the inversion process while simultaneously achieving an accuracy of 0.05 g/cm^(3) for the cement azimuthal density.This accuracy level is ten times higher compared to density accuracy calculated using calibration equations.Overall,this algorithm enhances the accuracy of cement azimuthal density evaluation,provides valuable technical support for the monitoring of cement azimuthal density in the oil and gas industry.展开更多
A fourth-order convergence method of solving roots for nonlinear equation, which is a variant of Newton's method given. Its convergence properties is proved. It is at least fourth-order convergence near simple roots ...A fourth-order convergence method of solving roots for nonlinear equation, which is a variant of Newton's method given. Its convergence properties is proved. It is at least fourth-order convergence near simple roots and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton and Newton-type methods. The results show that the proposed method has some more advantages than others. It enriches the methods to find the roots of non-linear equations and it is important in both theory and application.展开更多
A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is g...A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is given, which shows that the same order of accuracy can be achieved as solving the system directly in the fine mesh when h = H2. Both theoretical analysis and numerical experiments illustrate the efficiency of the algorithm for solving the coupled problem.展开更多
In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinea...In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems (with same stiffness matrix but different right-hand side) on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.展开更多
Air exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2nd century BC, known as the rule of double false position in the West is given. In addition to pointing out that the rule of dou...Air exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2nd century BC, known as the rule of double false position in the West is given. In addition to pointing out that the rule of double false position is actually a translation version of the ancient Chinese algorithm, a comparison with well-known Newton iteration method is also made. If derivative is introduced, the ancient Chinese algorithm reduces to the Newton method. A modification of the ancient Chinese algorithm is also proposed, and some of applications to nonlinear oscillators are illustrated.展开更多
Non equiripple approximation of filter characteristics can be realized either odd order or even order in the symmetric load case.This paper presents a method of synthesizing non equiripple low pass filter based on ...Non equiripple approximation of filter characteristics can be realized either odd order or even order in the symmetric load case.This paper presents a method of synthesizing non equiripple low pass filter based on iteration analysis,in which the rational fraction formed of Chebyshev polynomial is used as the filter characteristic function.This method is convenient for computer programming,because the attenuation zeros and poles of the filter can be determined easily and the synthesis procedure is simple,too.The given examples show that the method is of a practical value in filter design.展开更多
By analyzing the characteristics of low Mach number perfect gas flows, a novel Slightly Compressible Model (SCM) for low Mach number perect gas flows is derived. In view of numerical calculations, this model is proved...By analyzing the characteristics of low Mach number perfect gas flows, a novel Slightly Compressible Model (SCM) for low Mach number perect gas flows is derived. In view of numerical calculations, this model is proved very efficient, for it is kept within thep-v frame but does not have to satisfy the time consuming divergence-free condition in order to get the incompressible Navier-Stokes equation solution. Writing the equations in the form of conservation laws, we have derived the characteristic systems which are necessary for numerical calculations. A cell-centered finite-volume method with flux difference upwind-biased schemes is used for the equation solutions and a new Exact Newton Relaxation (ENR) implicit method is developed. Various computed results are presented to validate the present model. Laminar flow solutions over a circular cylinder with wake developing and vortex shedding are presented. Results for inviscid flow over a sphere are compared in excellent agreement with the exact analytic incompressible solution. Three-dimensional viscous flow solutions over sphere and prolate spheroid are also calculated and compared well with experiments and other incompressible solutions. Finally, good convergent performances are shown for sphere viscous flows.展开更多
Equivalent staggered-grid(ESG) as a new family of schemes has been utilized in seismic modeling,imaging,and inversion.Traditionally,the Taylor series expansion is often applied to calculate finite-difference(FD) coeff...Equivalent staggered-grid(ESG) as a new family of schemes has been utilized in seismic modeling,imaging,and inversion.Traditionally,the Taylor series expansion is often applied to calculate finite-difference(FD) coefficients on spatial derivatives,but the simulation results suffer serious numerical dispersion on a large frequency zone.We develop an optimized equivalent staggered-grid(OESG) FD method that can simultaneously suppress temporal and spatial dispersion for solving the second-order system of the 3 D elastic wave equation.On the one hand,we consider the coupling relations between wave speeds and spatial derivatives in the elastic wave equation and give three sets of FD coefficients with respect to the P-wave,S-wave,and converted-wave(C-wave) terms.On the other hand,a novel plane wave solution for the 3 D elastic wave equation is derived from the matrix decomposition method to construct the time-space dispersion relations.FD coefficients of the OESG method can be acquired by solving the new dispersion equations based on the Newton iteration method.Finally,we construct a new objective function to analyze P-wave,S-wave,and C-wave dispersion concerning frequencies.The dispersion analyses show that the presented method produces less modeling errors than the traditional ESG method.The synthetic examples demonstrate the effectiveness and superiority of the presented method.展开更多
Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability ...Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.展开更多
The dynamic calculations of slender marine risers, such as Finite Element Method (FEM) or Modal Expansion Solution Method (MESM), are mainly for the slender structures with their both ends hinged to the surface an...The dynamic calculations of slender marine risers, such as Finite Element Method (FEM) or Modal Expansion Solution Method (MESM), are mainly for the slender structures with their both ends hinged to the surface and bottom. However, for the re-entry operation, risers held by vessels are in vertical free hanging state, so the displacement and velocity of lower joint would not be zero. For the model of free hanging flexible marine risers, the paper proposed a Finite Difference Approximation (FDA) method for its dynamic calculation. The riser is divided into a reasonable number of rigid discrete segments. And the dynamic model is established based on simple Euler-Bemoulli Beam Theory concerning tension, shear forces and bending moments at each node along the cylindrical structures, which is extendible for different boundary conditions. The governing equations with specific boundary conditions for riser's free hanging state are simplified by Keller-box method and solved with Newton iteration algorithm for a stable dynamic solution. The calculation starts when the riser is vertical and still in calm water, and its behavior is obtained along time responding to the lateral forward motion at the top. The dynamic behavior in response to the lateral parametric excitation at the top is also proposed and discussed in this paper.展开更多
A complex, square matrix E is called coninvolutory if EE = I, where E denotes complex conjugate of the matrix E and I is an identity matrix. In this paper we introduce the coninvolutory decomposition of a complex matr...A complex, square matrix E is called coninvolutory if EE = I, where E denotes complex conjugate of the matrix E and I is an identity matrix. In this paper we introduce the coninvolutory decomposition of a complex matrix and investigate a Newton iteration for computing the coninvolutory factor. A simple numerical example illustrates our results.展开更多
Kantorovich theorem was extended to variational inequalities by which the convergence of Newton iteration,the existence and uniqueness of the solution of the problem can be tested via computational conditions at the i...Kantorovich theorem was extended to variational inequalities by which the convergence of Newton iteration,the existence and uniqueness of the solution of the problem can be tested via computational conditions at the initial point.展开更多
The magnetoresistance effect of a p-n junction under an electric field which is introduced by the gate voltage at room temperature is investigated by simulation. As auxiliary models, the Lombardi CVT model and carrier...The magnetoresistance effect of a p-n junction under an electric field which is introduced by the gate voltage at room temperature is investigated by simulation. As auxiliary models, the Lombardi CVT model and carrier generation- recombination model are introduced into a drift-diffusion transport model and carrier continuity equations. All the equa- tions are discretized by the finite-difference method and the box integration method and then solved by Newton iteration. Taking advantage of those models and methods, an abrupt junction with uniform doping is studied systematically, and the magnetoresistance as a function of doping concentration, SiO2 thickness and geometrical size is also investigated. The simulation results show that the magnetoresistance (MR) can be controlled substantially by the gate and is dependent on the polarity of the magnetic field.展开更多
This paper presents mechanical quadrature methods (MQMs) for solving nonlinear boundary Helmholtz integral equations. The methods have high accuracy of order O(h3) and low computation complexity. Moreover, the mec...This paper presents mechanical quadrature methods (MQMs) for solving nonlinear boundary Helmholtz integral equations. The methods have high accuracy of order O(h3) and low computation complexity. Moreover, the mechanical quadrature methods are simple without computing any singular integration. A nonlinear system is constructed by discretizing the nonlinear boundary integral equations. The stability and convergence of the system are proved based on an asymptotical compact theory and the Stepleman theorem. Using the h3-Richardson extrapolation algorithms (EAs), the accuracy to the order of O(h5) is improved. To slove the nonlinear system, the Newton iteration is discussed extensively by using the Ostrowski fixed point theorem. The efficiency of the algorithms is illustrated by numerical examples.展开更多
Independent component analysis (ICA) is the primary statistical method for solving the problems of blind source separation. The fast ICA is a famous and excellent algorithm and its contrast function is optimized by ...Independent component analysis (ICA) is the primary statistical method for solving the problems of blind source separation. The fast ICA is a famous and excellent algorithm and its contrast function is optimized by the quadratic convergence of Newton iteration method. In order to improve the convergence speed and the separation precision of the fast ICA, an improved fast ICA algorithm is presented. The algorithm introduces an efficient Newton's iterative method with fifth-order convergence for optimizing the contrast function and gives the detail derivation process and the corresponding condition. The experimental results demonstrate that the convergence speed and the separation precision of the improved algorithm are better than that of the fast ICA.展开更多
In this paper,we propose a Newton iterative algorithm to numerically reconstruct a locally rough surface with Dirichlet and impedance boundary conditions by near-field measurements of acoustic waves.The algorithm reli...In this paper,we propose a Newton iterative algorithm to numerically reconstruct a locally rough surface with Dirichlet and impedance boundary conditions by near-field measurements of acoustic waves.The algorithm relies on the Frechet differentiability analysis of the locally rough surface scattering problem,which is established by reducing the original model into an equivalent boundary value problem with compactly supported boundary data.With a slight modification,the algorithm can be also extended to reconstruct the local perturbation of a non-local rough surface.Finally,numerical results are presented to illustrate the effectiveness of the inversion algorithm with the multi-frequency data.展开更多
The fixed-point algorithm and infomax algorithm are two of the most popular algorithms in independent component analysis(ICA).However,it is hard to take both stability and speed into consideration in processing functi...The fixed-point algorithm and infomax algorithm are two of the most popular algorithms in independent component analysis(ICA).However,it is hard to take both stability and speed into consideration in processing functional magnetic resonance imaging(fMRI)data.In this paper,an optimization model for ICA is presented and an improved fixed-point algorithm based on the model is proposed.In the new algorithms a small step size is added to increase the stability.In order to accelerate the convergence,an improvement on Newton method is made,which makes cubic convergence for the new algorithm.Applying the algorithm and two other algorithms to invivo fMRI data,the results show that the new algorithm separates independent components stably,which has faster convergence speed and less computation than the other two algorithms.The algorithm has obvious advantage in processing fMRI signal with huge data.展开更多
Newton's iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the...Newton's iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix, the matrix-vector multiplication involved in Newton's iteration can be done efficiently. We show that the convergence of the modified Newton iteration is still very fast. Numerical results are presented to demonstrate the fast convergence of the proposed method.展开更多
基金This study was supported by the“High level research and training project for professional leaders of teachers in Higher Vocational Colleges in Jiangsu Province”.
文摘In order to improve the performance of time difference of arrival(TDOA)localization,a nonlinear least squares algorithm is proposed in this paper.Firstly,based on the criterion of the minimized sum of square error of time difference of arrival,the location estimation is expressed as an optimal problem of a non-linear programming.Then,an initial point is obtained using the semi-definite programming.And finally,the location is extracted from the local optimal solution acquired by Newton iterations.Simulation results show that when the number of anchor nodes is large,the performance of the proposed algorithm will be significantly better than that of semi-definite programming approach with the increase of measurement noise.
基金supported by the National Natural Science Foundation of China(No.11271298)
文摘This paper considers Stokes and Newton iterations to solve stationary Navier- Stokes equations based on the finite element discretization. We obtain new sufficient conditions of stability and convergence for the two iterations. Specifically, when 0 〈 σ =N||f||-1/v2≤1/√2+1 , the Stokes iteration is stable and convergent, where N is defined in the paper. When 0 〈 σ ≤5/11, the Newton iteration is stable and convergent. This work gives a more accurate admissible range of data for stability and convergence of the two schemes, which improves the previous results. A numerical test is given to verify the theory.
基金The authors would like to acknowledge the support of the National Natural Science Foundation of China(41974127,42174147).References。
文摘Cement density monitoring plays a vital role in evaluating the quality of cementing projects,which is of great significance to the development of oil and gas.However,the presence of inhomogeneous cement distribution and casing eccentricity in horizontal wells often complicates the accurate evaluation of cement azimuthal density.In this regard,this paper proposes an algorithm to calculate the cement azimuthal density in horizontal wells using a multi-detector gamma-ray detection system.The spatial dynamic response functions are simulated to obtain the influence of cement density on gamma-ray counts by the perturbation theory,and the contribution of cement density in six sectors to the gamma-ray recorded by different detectors is obtained by integrating the spatial dynamic response functions.Combined with the relationship between gamma-ray counts and cement density,a multi-parameter calculation equation system is established,and the regularized Newton iteration method is employed to invert casing eccentricity and cement azimuthal density.This approach ensures the stability of the inversion process while simultaneously achieving an accuracy of 0.05 g/cm^(3) for the cement azimuthal density.This accuracy level is ten times higher compared to density accuracy calculated using calibration equations.Overall,this algorithm enhances the accuracy of cement azimuthal density evaluation,provides valuable technical support for the monitoring of cement azimuthal density in the oil and gas industry.
基金Foundation item: Supported by the National Science Foundation of China(10701066) Supported by the National Foundation of the Education Department of Henan Province(2008A110022)
文摘A fourth-order convergence method of solving roots for nonlinear equation, which is a variant of Newton's method given. Its convergence properties is proved. It is at least fourth-order convergence near simple roots and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton and Newton-type methods. The results show that the proposed method has some more advantages than others. It enriches the methods to find the roots of non-linear equations and it is important in both theory and application.
基金supported by National Foundation of Natural Science(11471092,11326231)Zhejiang Provincial Natural Science Foundation of China(LZ13A010003)
文摘A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is given, which shows that the same order of accuracy can be achieved as solving the system directly in the fine mesh when h = H2. Both theoretical analysis and numerical experiments illustrate the efficiency of the algorithm for solving the coupled problem.
基金supported by National Foundation of Natural Science under the Grant 11071216
文摘In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems (with same stiffness matrix but different right-hand side) on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.
文摘Air exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2nd century BC, known as the rule of double false position in the West is given. In addition to pointing out that the rule of double false position is actually a translation version of the ancient Chinese algorithm, a comparison with well-known Newton iteration method is also made. If derivative is introduced, the ancient Chinese algorithm reduces to the Newton method. A modification of the ancient Chinese algorithm is also proposed, and some of applications to nonlinear oscillators are illustrated.
文摘Non equiripple approximation of filter characteristics can be realized either odd order or even order in the symmetric load case.This paper presents a method of synthesizing non equiripple low pass filter based on iteration analysis,in which the rational fraction formed of Chebyshev polynomial is used as the filter characteristic function.This method is convenient for computer programming,because the attenuation zeros and poles of the filter can be determined easily and the synthesis procedure is simple,too.The given examples show that the method is of a practical value in filter design.
基金The project supported by the Basic Research on Frontier Problems in Fluid and Aerodynamics in Chinathe National Natural Science Foundation of China (19772069)
文摘By analyzing the characteristics of low Mach number perfect gas flows, a novel Slightly Compressible Model (SCM) for low Mach number perect gas flows is derived. In view of numerical calculations, this model is proved very efficient, for it is kept within thep-v frame but does not have to satisfy the time consuming divergence-free condition in order to get the incompressible Navier-Stokes equation solution. Writing the equations in the form of conservation laws, we have derived the characteristic systems which are necessary for numerical calculations. A cell-centered finite-volume method with flux difference upwind-biased schemes is used for the equation solutions and a new Exact Newton Relaxation (ENR) implicit method is developed. Various computed results are presented to validate the present model. Laminar flow solutions over a circular cylinder with wake developing and vortex shedding are presented. Results for inviscid flow over a sphere are compared in excellent agreement with the exact analytic incompressible solution. Three-dimensional viscous flow solutions over sphere and prolate spheroid are also calculated and compared well with experiments and other incompressible solutions. Finally, good convergent performances are shown for sphere viscous flows.
文摘Equivalent staggered-grid(ESG) as a new family of schemes has been utilized in seismic modeling,imaging,and inversion.Traditionally,the Taylor series expansion is often applied to calculate finite-difference(FD) coefficients on spatial derivatives,but the simulation results suffer serious numerical dispersion on a large frequency zone.We develop an optimized equivalent staggered-grid(OESG) FD method that can simultaneously suppress temporal and spatial dispersion for solving the second-order system of the 3 D elastic wave equation.On the one hand,we consider the coupling relations between wave speeds and spatial derivatives in the elastic wave equation and give three sets of FD coefficients with respect to the P-wave,S-wave,and converted-wave(C-wave) terms.On the other hand,a novel plane wave solution for the 3 D elastic wave equation is derived from the matrix decomposition method to construct the time-space dispersion relations.FD coefficients of the OESG method can be acquired by solving the new dispersion equations based on the Newton iteration method.Finally,we construct a new objective function to analyze P-wave,S-wave,and C-wave dispersion concerning frequencies.The dispersion analyses show that the presented method produces less modeling errors than the traditional ESG method.The synthetic examples demonstrate the effectiveness and superiority of the presented method.
基金Project(50978112) supported by the National Natural Science Foundation of China
文摘Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.
基金supported and sponsored jointly by the National Natural Science Foundation of China(Grand Nos.51009092 and 50909061)Doctoral Foundation of the Ministry of Education of China(Grand No.20090073120013)the National High Technology Research and Development Program of China(863Program,Grand No.2008AA092301-1)
文摘The dynamic calculations of slender marine risers, such as Finite Element Method (FEM) or Modal Expansion Solution Method (MESM), are mainly for the slender structures with their both ends hinged to the surface and bottom. However, for the re-entry operation, risers held by vessels are in vertical free hanging state, so the displacement and velocity of lower joint would not be zero. For the model of free hanging flexible marine risers, the paper proposed a Finite Difference Approximation (FDA) method for its dynamic calculation. The riser is divided into a reasonable number of rigid discrete segments. And the dynamic model is established based on simple Euler-Bemoulli Beam Theory concerning tension, shear forces and bending moments at each node along the cylindrical structures, which is extendible for different boundary conditions. The governing equations with specific boundary conditions for riser's free hanging state are simplified by Keller-box method and solved with Newton iteration algorithm for a stable dynamic solution. The calculation starts when the riser is vertical and still in calm water, and its behavior is obtained along time responding to the lateral forward motion at the top. The dynamic behavior in response to the lateral parametric excitation at the top is also proposed and discussed in this paper.
基金Supported by the Natural Science Foundation of Guangdong Province(91510631000021,s2012010009985)Research Fund for the Doctoral Program of Higher Education of China(20104407110001)the National Natural Science Foundation of China(11271144,10971075,and 11101164)
文摘A complex, square matrix E is called coninvolutory if EE = I, where E denotes complex conjugate of the matrix E and I is an identity matrix. In this paper we introduce the coninvolutory decomposition of a complex matrix and investigate a Newton iteration for computing the coninvolutory factor. A simple numerical example illustrates our results.
文摘Kantorovich theorem was extended to variational inequalities by which the convergence of Newton iteration,the existence and uniqueness of the solution of the problem can be tested via computational conditions at the initial point.
文摘The magnetoresistance effect of a p-n junction under an electric field which is introduced by the gate voltage at room temperature is investigated by simulation. As auxiliary models, the Lombardi CVT model and carrier generation- recombination model are introduced into a drift-diffusion transport model and carrier continuity equations. All the equa- tions are discretized by the finite-difference method and the box integration method and then solved by Newton iteration. Taking advantage of those models and methods, an abrupt junction with uniform doping is studied systematically, and the magnetoresistance as a function of doping concentration, SiO2 thickness and geometrical size is also investigated. The simulation results show that the magnetoresistance (MR) can be controlled substantially by the gate and is dependent on the polarity of the magnetic field.
基金supported by the National Natural Science Foundation of China(No.10871034)the Natural Science Foundation Project of Chongqing(No.CSTC20-10BB8270)+1 种基金the Air Force Office of Scientific Research(No.FA9550-08-1-0136)the National Science Foundation(No.OCE-0620464)
文摘This paper presents mechanical quadrature methods (MQMs) for solving nonlinear boundary Helmholtz integral equations. The methods have high accuracy of order O(h3) and low computation complexity. Moreover, the mechanical quadrature methods are simple without computing any singular integration. A nonlinear system is constructed by discretizing the nonlinear boundary integral equations. The stability and convergence of the system are proved based on an asymptotical compact theory and the Stepleman theorem. Using the h3-Richardson extrapolation algorithms (EAs), the accuracy to the order of O(h5) is improved. To slove the nonlinear system, the Newton iteration is discussed extensively by using the Ostrowski fixed point theorem. The efficiency of the algorithms is illustrated by numerical examples.
文摘Independent component analysis (ICA) is the primary statistical method for solving the problems of blind source separation. The fast ICA is a famous and excellent algorithm and its contrast function is optimized by the quadratic convergence of Newton iteration method. In order to improve the convergence speed and the separation precision of the fast ICA, an improved fast ICA algorithm is presented. The algorithm introduces an efficient Newton's iterative method with fifth-order convergence for optimizing the contrast function and gives the detail derivation process and the corresponding condition. The experimental results demonstrate that the convergence speed and the separation precision of the improved algorithm are better than that of the fast ICA.
文摘In this paper,we propose a Newton iterative algorithm to numerically reconstruct a locally rough surface with Dirichlet and impedance boundary conditions by near-field measurements of acoustic waves.The algorithm relies on the Frechet differentiability analysis of the locally rough surface scattering problem,which is established by reducing the original model into an equivalent boundary value problem with compactly supported boundary data.With a slight modification,the algorithm can be also extended to reconstruct the local perturbation of a non-local rough surface.Finally,numerical results are presented to illustrate the effectiveness of the inversion algorithm with the multi-frequency data.
文摘The fixed-point algorithm and infomax algorithm are two of the most popular algorithms in independent component analysis(ICA).However,it is hard to take both stability and speed into consideration in processing functional magnetic resonance imaging(fMRI)data.In this paper,an optimization model for ICA is presented and an improved fixed-point algorithm based on the model is proposed.In the new algorithms a small step size is added to increase the stability.In order to accelerate the convergence,an improvement on Newton method is made,which makes cubic convergence for the new algorithm.Applying the algorithm and two other algorithms to invivo fMRI data,the results show that the new algorithm separates independent components stably,which has faster convergence speed and less computation than the other two algorithms.The algorithm has obvious advantage in processing fMRI signal with huge data.
基金Research supported in part by the National Natural Science Foundation of China under grant 10471027 and Shanghai Education Committee, RGC 7046/03P, 7035/04P, 7045/05P and HKBU FRGs.The authors would like to thank the referees for their useful suggestions.
文摘Newton's iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix, the matrix-vector multiplication involved in Newton's iteration can be done efficiently. We show that the convergence of the modified Newton iteration is still very fast. Numerical results are presented to demonstrate the fast convergence of the proposed method.