The authors proposed a symplectic stereo-modeling method(SSM)in the Birkhoffian dynam-ics and apply it to the visco-acoustic least-squares reverse time migration(LSRTM).The SSM adopts ste-reo-modeling operator in spac...The authors proposed a symplectic stereo-modeling method(SSM)in the Birkhoffian dynam-ics and apply it to the visco-acoustic least-squares reverse time migration(LSRTM).The SSM adopts ste-reo-modeling operator in space and symplectic Runge-Kutta scheme in time,resulting in great ability in suppressing numerical dispersion and long-time computing.These advantages are further confirmed by numerical dispersion analysis,long-time computation test and computational efficiency comparison.After these theoretical analyses and experiments,acoustic and visco-acoustic LSRTM are tested and compared between SSM method and the conventional symplectic method(CSM)using the fault and marmousi models.Meanwhile,dynamic source encoding and exponential decay moving average gradients method are adopted to reduce the computation cost and improve the convergence rate.The imaging results show that LSRTM based on visco-acoustic wave equations effectively takes into account the influence of viscosity can therefore compensate for the amplitude attenuation.Besides,SSM method not only has high numerical accuracy and computational efficiency,but also performs effectively in LSRTM.展开更多
Simultaneous-source acquisition has been recog- nized as an economic and efficient acquisition method, but the direct imaging of the simultaneous-source data produces migration artifacts because of the interference of...Simultaneous-source acquisition has been recog- nized as an economic and efficient acquisition method, but the direct imaging of the simultaneous-source data produces migration artifacts because of the interference of adjacent sources. To overcome this problem, we propose the regularized least-squares reverse time migration method (RLSRTM) using the singular spectrum analysis technique that imposes sparseness constraints on the inverted model. Additionally, the difference spectrum theory of singular values is presented so that RLSRTM can be implemented adaptively to eliminate the migration artifacts. With numerical tests on a fiat layer model and a Marmousi model, we validate the superior imaging quality, efficiency and convergence of RLSRTM compared with LSRTM when dealing with simultaneoussource data, incomplete data and noisy data.展开更多
The full-spectrum least-squares(FSLS) method is introduced to perform quantitative energy-dispersive X-ray fluorescence analysis for unknown solid samples.Based on the conventional least-squares principle, this spectr...The full-spectrum least-squares(FSLS) method is introduced to perform quantitative energy-dispersive X-ray fluorescence analysis for unknown solid samples.Based on the conventional least-squares principle, this spectrum evaluation method is able to obtain the background-corrected and interference-free net peaks, which is significant for quantization analyses. A variety of analytical parameters and functions to describe the features of the fluorescence spectra of pure elements are used and established, such as the mass absorption coefficient, the Gi factor, and fundamental fluorescence formulas. The FSLS iterative program was compiled in the C language. The content of each component should reach the convergence criterion at the end of the calculations. After a basic theory analysis and experimental preparation, 13 national standard soil samples were detected using a spectrometer to test the feasibility of using the algorithm. The results show that the calculated contents of Ti, Fe, Ni, Cu, and Zn have the same changing tendency as the corresponding standard content in the 13 reference samples. Accuracies of 0.35% and 14.03% are obtained, respectively, for Fe and Ti, whose standard concentrations are 8.82% and 0.578%, respectively. However, the calculated results of trace elements (only tens of lg/g) deviate from the standard values. This may be because of measurement accuracy and mutual effects between the elements.展开更多
The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features becau...The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.展开更多
The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of t...The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of the same type: In a breakdown situation the Galerkin method is unable to calculate an approximate solution, while the least-squares method, although does not really break down, is unsucessful in reducing the norm of its residual. In this paper we first establish a unified theorem which gives a relationship between breakdowns in the two methods. We further illustrate theoretically and experimentally that if the coefficient matrix of a lienar system is of high defectiveness with the associated eigenvalues less than 1, then the restarted Galerkin and least-squares methods will be in great risks of complete breakdowns. It appears that our findings may help to understand phenomena observed practically and to derive treatments for breakdowns of this type.展开更多
Numerical solution of shallow-water equations (SWE) has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of s...Numerical solution of shallow-water equations (SWE) has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include: the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.展开更多
The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not...The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi (LBB) condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1(Ω).展开更多
The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-pr...The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.展开更多
In several LUCC studies, statistical methods are being used to analyze land use data. A problem using conventional statistical methods in land use analysis is that these methods assume the data to be statistically ind...In several LUCC studies, statistical methods are being used to analyze land use data. A problem using conventional statistical methods in land use analysis is that these methods assume the data to be statistically independent. But in fact, they have the tendency to be dependent, a phenomenon known as multicollinearity, especially in the cases of few observations. In this paper, a Partial Least-Squares (PLS) regression approach is developed to study relationships between land use and its influencing factors through a case study of the Suzhou-Wuxi-Changzhou region in China. Multicollinearity exists in the dataset and the number of variables is high compared to the number of observations. Four PLS factors are selected through a preliminary analysis. The correlation analyses between land use and influencing factors demonstrate the land use character of rural industrialization and urbanization in the Suzhou-Wuxi-Changzhou region, meanwhile illustrate that the first PLS factor has enough ability to best describe land use patterns quantitatively, and most of the statistical relations derived from it accord with the fact. By the decreasing capacity of the PLS factors, the reliability of model outcome decreases correspondingly.展开更多
A novel algorithm for source location by utilizing the time difference of arrival (TDOA) measurements of a signal received at spatially separated sensors is proposed. The algorithm is based on quadratic constraint tot...A novel algorithm for source location by utilizing the time difference of arrival (TDOA) measurements of a signal received at spatially separated sensors is proposed. The algorithm is based on quadratic constraint total least-squares (QC-TLS) method and gives an explicit solution. The total least-squares method is a generalized data fitting method that is appropriate for cases when the system model contains error or is not known exactly, and quadratic constraint, which could be realized via Lagrange multipliers technique, could constrain the solution to the location equations to improve location accuracy. Comparisons of performance with ordinary least-squares are made, and Monte Carlo simulations are performed. Simulation results indicate that the proposed algorithm has high location accuracy and achieves accuracy close to the Cramer-Rao lower bound (CRLB) near the small TDOA measurement error region.展开更多
This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obt...This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obtained in T = n(log2m + log2(n - r + 1) + 5) + log2m + 1 steps with P=mn processors when m × 2(n - 1) and with P = 2n(n - 1) processors otherwise.展开更多
Necessary and sufficient conditions are derived for some matrix equations that have a common least-squares solution.A general expression is provided when certain resolvable conditions are satisfied.This research exten...Necessary and sufficient conditions are derived for some matrix equations that have a common least-squares solution.A general expression is provided when certain resolvable conditions are satisfied.This research extends existing work in the literature.展开更多
Order-recursive least-squares(ORLS)algorithms are applied to the prob-lems of estimation and identification of FIR or ARMA system parameters where a fixedset of input signal samples is available and the desired order ...Order-recursive least-squares(ORLS)algorithms are applied to the prob-lems of estimation and identification of FIR or ARMA system parameters where a fixedset of input signal samples is available and the desired order of the underlying model isunknown.On the basis of several universal formulae for updating nonsymmetric projec-tion operators,this paper presents three kinds of LS algorithms,called nonsymmetric,symmetric and square root normalized fast ORLS algorithms,respectively.As to the au-thors’ knowledge,the first and the third have not been so far provided,and the second isone of those which have the lowest computational requirement.Several simplified versionsof the algorithms are also considered.展开更多
A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary ...A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary equation, optimal H-t and L-2-error estimates are derived under the standard regularity assumption on the finite element partition ( the LBB-condition is not required). Far the evolutionary equation, optimal L-2 estimates are derived under the conventional Raviart-Thomas spaces.展开更多
A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approxi...A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori error estimator. The posteriori errors are effectively estimated. The convergence of the adaptive least-squares mixed finite element method is proved.展开更多
The UV absorption spectra of o-naphthol,α-naphthylamine,2,7-dihydroxy naphthalene,2,4-dimethoxy ben- zaldehyde and methyl salicylate,overlap severely;therefore it is impossible to determine them in mixtures by tradit...The UV absorption spectra of o-naphthol,α-naphthylamine,2,7-dihydroxy naphthalene,2,4-dimethoxy ben- zaldehyde and methyl salicylate,overlap severely;therefore it is impossible to determine them in mixtures by traditional spectrophotometric methods.In this paper,the partial least-squares(PLS)regression is applied to the simultaneous determination of these compounds in mixtures by UV spectrophtometry without any pretreatment of the samples.Ten synthetic mixture samples are analyzed by the proposed method.The mean recoveries are 99.4%,996%,100.2%,99.3% and 99.1%,and the relative standard deviations(RSD) are 1.87%,1.98%,1.94%,0.960% and 0.672%,respectively.展开更多
In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the line...In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the linearized version of the viscoelastic UCM model. The L2 least-squares functional involves the residuals of each equation multiplied by proper weights. The corresponding homogeneous functional is equivalent to a natural norm. The error estimates of the finite element solution are analyzed when the conforming piecewise polynomial elements are used for the unknowns.展开更多
Estimation of stochastic demand in physical distribution in general and efficient transport routs management in particular is emerging as a crucial factor in urban planning domain. It is particularly important in some...Estimation of stochastic demand in physical distribution in general and efficient transport routs management in particular is emerging as a crucial factor in urban planning domain. It is particularly important in some municipalities such as Tehran where a sound demand management calls for a realistic analysis of the routing system. The methodology involved critically investigating a fuzzy least-squares linear regression approach (FLLRs) to estimate the stochastic demands in the vehicle routing problem (VRP) bearing in mind the customer's preferences order. A FLLR method is proposed in solving the VRP with stochastic demands: approximate-distance fuzzy least-squares (ADFL) estimator ADFL estimator is applied to original data taken from a case study. The SSR values of the ADFL estimator and real demand are obtained and then compared to SSR values of the nominal demand and real demand. Empirical results showed that the proposed method can be viable in solving problems under circumstances of having vague and imprecise performance ratings. The results further proved that application of the ADFL was realistic and efficient estimator to face the sto- chastic demand challenges in vehicle routing system management and solve relevant problems.展开更多
Background:This article investigates the Least-Squares Monte Carlo Method by using different polynomial basis in American Asian Options pricing.The standard approach in the option pricing literature is to choose the b...Background:This article investigates the Least-Squares Monte Carlo Method by using different polynomial basis in American Asian Options pricing.The standard approach in the option pricing literature is to choose the basis arbitrarily.By comparing four different polynomial basis we show that the choice of basis interferes in the option's price.Methods:We assess Least-Squares Method performance in pricing four different American Asian Options by using four polynomial basis:Power,Laguerre,Legendre and Hermite A.To every American Asian Option priced,three sets of parameters are used in order to evaluate it properly.Results:We show that the choice of the basis interferes in the option's price by showing that one of them converges to the option's value faster than any other by using fewer simulated paths.In the case of an Amerasian call option,for example,we find that the preferable polynomial basis is Hermite A.For an Amerasian put option,the Power polynomial basis is recommended.Such empirical outcome is theoretically unpredictable,since in principle all basis can be indistinctly used when pricing the derivative.Conclusion:In this article The Least-Squares Monte Carlo Method performance is assessed in pricing four different types of American Asian Options by using four different polynomial basis through three different sets of parameters.Our results suggest that one polynomial basis is best suited to perform the method when pricing an American Asian option.Theoretically all basis can be indistinctly used when pricing the derivative.However,our results does not confirm these.We find that when pricing an American Asian put option,Power A is better than the other basis we have studied here whereas when pricing an American Asian call,Hermite A is better.展开更多
基金Supported by projects of National Natural Science Foundation of China(Nos.41604105,41974114)Fundamental Research Funds for Central Universities(No.2020YQLX01).
文摘The authors proposed a symplectic stereo-modeling method(SSM)in the Birkhoffian dynam-ics and apply it to the visco-acoustic least-squares reverse time migration(LSRTM).The SSM adopts ste-reo-modeling operator in space and symplectic Runge-Kutta scheme in time,resulting in great ability in suppressing numerical dispersion and long-time computing.These advantages are further confirmed by numerical dispersion analysis,long-time computation test and computational efficiency comparison.After these theoretical analyses and experiments,acoustic and visco-acoustic LSRTM are tested and compared between SSM method and the conventional symplectic method(CSM)using the fault and marmousi models.Meanwhile,dynamic source encoding and exponential decay moving average gradients method are adopted to reduce the computation cost and improve the convergence rate.The imaging results show that LSRTM based on visco-acoustic wave equations effectively takes into account the influence of viscosity can therefore compensate for the amplitude attenuation.Besides,SSM method not only has high numerical accuracy and computational efficiency,but also performs effectively in LSRTM.
基金financial support from the National Natural Science Foundation of China (Grant Nos. 41104069, 41274124)National Key Basic Research Program of China (973 Program) (Grant No. 2014CB239006)+2 种基金National Science and Technology Major Project (Grant No. 2011ZX05014-001-008)the Open Foundation of SINOPEC Key Laboratory of Geophysics (Grant No. 33550006-15-FW2099-0033)the Fundamental Research Funds for the Central Universities (Grant No. 16CX06046A)
文摘Simultaneous-source acquisition has been recog- nized as an economic and efficient acquisition method, but the direct imaging of the simultaneous-source data produces migration artifacts because of the interference of adjacent sources. To overcome this problem, we propose the regularized least-squares reverse time migration method (RLSRTM) using the singular spectrum analysis technique that imposes sparseness constraints on the inverted model. Additionally, the difference spectrum theory of singular values is presented so that RLSRTM can be implemented adaptively to eliminate the migration artifacts. With numerical tests on a fiat layer model and a Marmousi model, we validate the superior imaging quality, efficiency and convergence of RLSRTM compared with LSRTM when dealing with simultaneoussource data, incomplete data and noisy data.
基金supported by the National Key R&D Project of China(No.2017YFC0602100)the National Natural Science Foundation of China(No.41774147)Sichuan Science and Technology Support Program(No.2015GZ0272)
文摘The full-spectrum least-squares(FSLS) method is introduced to perform quantitative energy-dispersive X-ray fluorescence analysis for unknown solid samples.Based on the conventional least-squares principle, this spectrum evaluation method is able to obtain the background-corrected and interference-free net peaks, which is significant for quantization analyses. A variety of analytical parameters and functions to describe the features of the fluorescence spectra of pure elements are used and established, such as the mass absorption coefficient, the Gi factor, and fundamental fluorescence formulas. The FSLS iterative program was compiled in the C language. The content of each component should reach the convergence criterion at the end of the calculations. After a basic theory analysis and experimental preparation, 13 national standard soil samples were detected using a spectrometer to test the feasibility of using the algorithm. The results show that the calculated contents of Ti, Fe, Ni, Cu, and Zn have the same changing tendency as the corresponding standard content in the 13 reference samples. Accuracies of 0.35% and 14.03% are obtained, respectively, for Fe and Ti, whose standard concentrations are 8.82% and 0.578%, respectively. However, the calculated results of trace elements (only tens of lg/g) deviate from the standard values. This may be because of measurement accuracy and mutual effects between the elements.
基金This project is supported by Research Foundation for Doctoral Program of Higher Education, China (No.98033532)
文摘The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.
文摘The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of the same type: In a breakdown situation the Galerkin method is unable to calculate an approximate solution, while the least-squares method, although does not really break down, is unsucessful in reducing the norm of its residual. In this paper we first establish a unified theorem which gives a relationship between breakdowns in the two methods. We further illustrate theoretically and experimentally that if the coefficient matrix of a lienar system is of high defectiveness with the associated eigenvalues less than 1, then the restarted Galerkin and least-squares methods will be in great risks of complete breakdowns. It appears that our findings may help to understand phenomena observed practically and to derive treatments for breakdowns of this type.
基金the National Science Council of Taiwan for funding this research (NSC 96-2221-E-019-061).
文摘Numerical solution of shallow-water equations (SWE) has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include: the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.
基金supported by the National Basic Research Program of China (2005CB321701)NSF of mathematics research special fund of Hebei Province(08M005)
文摘The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi (LBB) condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1(Ω).
基金supported by the National Natural Science Foundation of China(No.41874001 and No.41664001)Support Program for Outstanding Youth Talents in Jiangxi Province(No.20162BCB23050)National Key Research and Development Program(No.2016YFB0501405)。
文摘The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.
基金National Natural Science Foundation of China No.40301038
文摘In several LUCC studies, statistical methods are being used to analyze land use data. A problem using conventional statistical methods in land use analysis is that these methods assume the data to be statistically independent. But in fact, they have the tendency to be dependent, a phenomenon known as multicollinearity, especially in the cases of few observations. In this paper, a Partial Least-Squares (PLS) regression approach is developed to study relationships between land use and its influencing factors through a case study of the Suzhou-Wuxi-Changzhou region in China. Multicollinearity exists in the dataset and the number of variables is high compared to the number of observations. Four PLS factors are selected through a preliminary analysis. The correlation analyses between land use and influencing factors demonstrate the land use character of rural industrialization and urbanization in the Suzhou-Wuxi-Changzhou region, meanwhile illustrate that the first PLS factor has enough ability to best describe land use patterns quantitatively, and most of the statistical relations derived from it accord with the fact. By the decreasing capacity of the PLS factors, the reliability of model outcome decreases correspondingly.
文摘A novel algorithm for source location by utilizing the time difference of arrival (TDOA) measurements of a signal received at spatially separated sensors is proposed. The algorithm is based on quadratic constraint total least-squares (QC-TLS) method and gives an explicit solution. The total least-squares method is a generalized data fitting method that is appropriate for cases when the system model contains error or is not known exactly, and quadratic constraint, which could be realized via Lagrange multipliers technique, could constrain the solution to the location equations to improve location accuracy. Comparisons of performance with ordinary least-squares are made, and Monte Carlo simulations are performed. Simulation results indicate that the proposed algorithm has high location accuracy and achieves accuracy close to the Cramer-Rao lower bound (CRLB) near the small TDOA measurement error region.
基金This project is supported by the National Natural Science Foundation of China
文摘This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obtained in T = n(log2m + log2(n - r + 1) + 5) + log2m + 1 steps with P=mn processors when m × 2(n - 1) and with P = 2n(n - 1) processors otherwise.
文摘Necessary and sufficient conditions are derived for some matrix equations that have a common least-squares solution.A general expression is provided when certain resolvable conditions are satisfied.This research extends existing work in the literature.
文摘Order-recursive least-squares(ORLS)algorithms are applied to the prob-lems of estimation and identification of FIR or ARMA system parameters where a fixedset of input signal samples is available and the desired order of the underlying model isunknown.On the basis of several universal formulae for updating nonsymmetric projec-tion operators,this paper presents three kinds of LS algorithms,called nonsymmetric,symmetric and square root normalized fast ORLS algorithms,respectively.As to the au-thors’ knowledge,the first and the third have not been so far provided,and the second isone of those which have the lowest computational requirement.Several simplified versionsof the algorithms are also considered.
文摘A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary equation, optimal H-t and L-2-error estimates are derived under the standard regularity assumption on the finite element partition ( the LBB-condition is not required). Far the evolutionary equation, optimal L-2 estimates are derived under the conventional Raviart-Thomas spaces.
文摘A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori error estimator. The posteriori errors are effectively estimated. The convergence of the adaptive least-squares mixed finite element method is proved.
文摘The UV absorption spectra of o-naphthol,α-naphthylamine,2,7-dihydroxy naphthalene,2,4-dimethoxy ben- zaldehyde and methyl salicylate,overlap severely;therefore it is impossible to determine them in mixtures by traditional spectrophotometric methods.In this paper,the partial least-squares(PLS)regression is applied to the simultaneous determination of these compounds in mixtures by UV spectrophtometry without any pretreatment of the samples.Ten synthetic mixture samples are analyzed by the proposed method.The mean recoveries are 99.4%,996%,100.2%,99.3% and 99.1%,and the relative standard deviations(RSD) are 1.87%,1.98%,1.94%,0.960% and 0.672%,respectively.
文摘In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the linearized version of the viscoelastic UCM model. The L2 least-squares functional involves the residuals of each equation multiplied by proper weights. The corresponding homogeneous functional is equivalent to a natural norm. The error estimates of the finite element solution are analyzed when the conforming piecewise polynomial elements are used for the unknowns.
文摘Estimation of stochastic demand in physical distribution in general and efficient transport routs management in particular is emerging as a crucial factor in urban planning domain. It is particularly important in some municipalities such as Tehran where a sound demand management calls for a realistic analysis of the routing system. The methodology involved critically investigating a fuzzy least-squares linear regression approach (FLLRs) to estimate the stochastic demands in the vehicle routing problem (VRP) bearing in mind the customer's preferences order. A FLLR method is proposed in solving the VRP with stochastic demands: approximate-distance fuzzy least-squares (ADFL) estimator ADFL estimator is applied to original data taken from a case study. The SSR values of the ADFL estimator and real demand are obtained and then compared to SSR values of the nominal demand and real demand. Empirical results showed that the proposed method can be viable in solving problems under circumstances of having vague and imprecise performance ratings. The results further proved that application of the ADFL was realistic and efficient estimator to face the sto- chastic demand challenges in vehicle routing system management and solve relevant problems.
文摘Background:This article investigates the Least-Squares Monte Carlo Method by using different polynomial basis in American Asian Options pricing.The standard approach in the option pricing literature is to choose the basis arbitrarily.By comparing four different polynomial basis we show that the choice of basis interferes in the option's price.Methods:We assess Least-Squares Method performance in pricing four different American Asian Options by using four polynomial basis:Power,Laguerre,Legendre and Hermite A.To every American Asian Option priced,three sets of parameters are used in order to evaluate it properly.Results:We show that the choice of the basis interferes in the option's price by showing that one of them converges to the option's value faster than any other by using fewer simulated paths.In the case of an Amerasian call option,for example,we find that the preferable polynomial basis is Hermite A.For an Amerasian put option,the Power polynomial basis is recommended.Such empirical outcome is theoretically unpredictable,since in principle all basis can be indistinctly used when pricing the derivative.Conclusion:In this article The Least-Squares Monte Carlo Method performance is assessed in pricing four different types of American Asian Options by using four different polynomial basis through three different sets of parameters.Our results suggest that one polynomial basis is best suited to perform the method when pricing an American Asian option.Theoretically all basis can be indistinctly used when pricing the derivative.However,our results does not confirm these.We find that when pricing an American Asian put option,Power A is better than the other basis we have studied here whereas when pricing an American Asian call,Hermite A is better.