A condition number is an amplification coefficient due to errors in computing. Thus the theory of condition numbers plays an important role in error analysis. In this paper, following the approach of Rice, condition n...A condition number is an amplification coefficient due to errors in computing. Thus the theory of condition numbers plays an important role in error analysis. In this paper, following the approach of Rice, condition numbers are defined for factors of some matrix factorizations such as the Cholesky factorization of a symmetric positive definite matrix and QR factorization of a general matrix. The condition numbers are derived by a technique of analytic expansion of the factor dependent on one parameter and matrix-vector equation. Condition numbers of the Cholesky and QR factors are different from the ones previously introduced by other authors, but similar to Chang's results. In Cholesky factorization, corresponding with the condition number of the factor matrix L , K _L is a low bound of Stewart's condition number K .展开更多
In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setti...In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setting the specific norms and weight parameters, we present the expressions of the structured normwise, mixed, componentwise condition numbers and the corresponding results for unstructured ones. In addition, we investigate the statistical estimation of condition numbers of LDU factorization using the probabilistic spectral norm estimator and the small-sample statistical condition estimation method, and devise three algorithms. Finally, we compare the structured condition numbers with the corresponding unstructured ones in numerical experiments.展开更多
In Multiple-Input Multiple-Out (MIMO) systems, the user selection algorithm plays an important role in the realization of multiplexing gain. In this paper, an improved Semi-orthogonal User Selection algorithm based ...In Multiple-Input Multiple-Out (MIMO) systems, the user selection algorithm plays an important role in the realization of multiplexing gain. In this paper, an improved Semi-orthogonal User Selection algorithm based on condition number is proposed. Besides, a new MIMO pre- coding scheme is designed. The proposed SUS- CN (SUS with condition number) algorithm outperforms the SUS algorithm for the selection of users with better matrix inversion property, thus a higher information rate for selected user pair is achieved. The designed MIMO precoding matrix brings benefits of the power equality at transmitted terminals, the limited dynamic range of the power over time, and a better power efficiency. The simulation results give the key insights into the im- pact of the different condition number value and users on the sum-rate capacity.展开更多
From the formulas of the conjugate gradient, a similarity between a symmetric positive definite (SPD) matrix A and a tridiagonal matrix B is obtained. The elements of the matrix B are determined by the parameters of t...From the formulas of the conjugate gradient, a similarity between a symmetric positive definite (SPD) matrix A and a tridiagonal matrix B is obtained. The elements of the matrix B are determined by the parameters of the conjugate gradient. The computation of eigenvalues of A is then reduced to the case of the tridiagonal matrix B. The approximation of extreme eigenvalues of A can be obtained as a 'by-product' in the computation of the conjugate gradient if a computational cost of O(s) arithmetic operations is added, where s is the number of iterations This computational cost is negligible compared with the conjugate gradient. If the matrix A is not SPD, the approximation of the condition number of A can be obtained from the computation of the conjugate gradient on AT A. Numerical results show that this is a convenient and highly efficient method for computing extreme eigenvalues and the condition number of nonsingular matrices.展开更多
In this paper,for the regularized Hermitian and skew-Hermitian splitting(RHSS)preconditioner introduced by Bai and Benzi(BIT Numer Math 57:287–311,2017)for the solution of saddle-point linear systems,we analyze the s...In this paper,for the regularized Hermitian and skew-Hermitian splitting(RHSS)preconditioner introduced by Bai and Benzi(BIT Numer Math 57:287–311,2017)for the solution of saddle-point linear systems,we analyze the spectral properties of the preconditioned matrix when the regularization matrix is a special Hermitian positive semidefinite matrix which depends on certain parameters.We accurately describe the numbers of eigenvalues clustered at(0,0)and(2,0),if the iteration parameter is close to 0.An estimate about the condition number of the corresponding eigenvector matrix,which partly determines the convergence rate of the RHSS-preconditioned Krylov subspace method,is also studied in this work.展开更多
The authors study the generation of matrices with complex entries belonging to some matrix groups, mainly those that are defined by a scalar product space. These matrices have useful applications in quantum mechanical...The authors study the generation of matrices with complex entries belonging to some matrix groups, mainly those that are defined by a scalar product space. These matrices have useful applications in quantum mechanical problems and complex control problems. In this work, the authors try to generate matrices such that: (1) the condition number of these types of matrices is controlled and (2) The algorithm used to generate these matrices preserves their structure.展开更多
In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias es...In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.展开更多
In the process of initial alignment for a strapdown inertial navigation system (SINS) on a stationary base, the east gyro drift rate is an important factor affecting the alignment accuracy of the azimuth misalignmen...In the process of initial alignment for a strapdown inertial navigation system (SINS) on a stationary base, the east gyro drift rate is an important factor affecting the alignment accuracy of the azimuth misalignment angle. When the Kalman filtering algorithm is adopted in initial alignment, it yields a constant error in the estimation of the azimuth misalignment angle because the east gyro drift rate cannot be estimated. To improve the alignment accuracy, a novel alignment method on revolving mounting base is proposed. The Kalman filtering algorithm of extending the measured values is studied. The theory of spectral condition number is utilized to analyze the degrees of observability of states. Simulation results show that the estimation accuracy of the azimuth misalignment angle is greatly improved through revolving mounting base, and the proposed method is efficient in initial alignment for a medium accurate SINS.展开更多
Diffusion tensor MRI (DT-MRI or DTI) is emerging as an important non-invasive technology for elucidating intemal brain structures. It has recently been utilized to diagnose a series of diseases that affect the integ...Diffusion tensor MRI (DT-MRI or DTI) is emerging as an important non-invasive technology for elucidating intemal brain structures. It has recently been utilized to diagnose a series of diseases that affect the integrity of neural systems to provide a basis for neuroregenerative studies. Results from the present study suggested that neural tissue is reconstructed with multiple diffusion-weighted gradient directions DTI, which varies from traditional imaging methods that utilize 6 gradient directions. Simultaneously, the diffusion tensor matrix is obtained by multiple linear regressions from an equation of echo signal intensity. The condition number value and standard deviation of fractional anisotropy for each scheme can be used to evaluate image quality. Results demonstrated that increasing gradient direction to some extent resulted in improved effects. Therefore, the traditional 6 and 15 directions should not be considered optimal scan protocols for clinical DTI application. In a scheme with 20 directions, the condition number and standard deviation of fractional anisotropy of the encoding gradients matrix were significantly reduced, and resulted in more clearly and accurately displayed neural tissue. Results demonstrated that the scheme with 20 diffusion gradient directions provided better accuracy of structural renderings and could be an optimal scan protocol for clinical DTI application.展开更多
The existing researches on singularity of parallel mechanism are mostly limited to the property and regularity of singularity locus and there is no further research into the geometric relationship between uncontrolled...The existing researches on singularity of parallel mechanism are mostly limited to the property and regularity of singularity locus and there is no further research into the geometric relationship between uncontrolled kinematic screw and parallel mechanism in singularity. A 3UPS-S parallel mechanism is presented which fulfils 3-DOF in rotation. The regularity of nutation angle singularity is analyzed based on the Jacobian matrix, and the singularity surface of 3UPS-S parallel mechanisms is obtained. By applying the concept of reciprocal product in screw theory, the singular kinematic screw is derived when 3UPS-S parallel mechanism is in singularity. The geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism is investigated by using programs in MATLAB. It is revealed that there are two kinds of situation. Firstly, the three limbs of 3UPS-S parallel mechanism intersect the singular kinematic screw in space simultaneously; Secondly, two limbs cross the singular kinematic screw while the third limb parallels with that screw. It is concluded that the nutation angle singularity of 3UPS-S parallel mechanism belongs to the singular linear complexes. This paper sheds light into and clarifies the geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism.展开更多
When linearizing three-dimensional(3 D)coordinate similarity transformation model with large rotations,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the...When linearizing three-dimensional(3 D)coordinate similarity transformation model with large rotations,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the problem,a series of conversions are contributed to the 3 D coordinate similarity transformation model in this paper.We deduced a complete solution for the 3 D coordinate similarity transformation at any rotation with the nonlinear adjustment methodology,which involves the errors of the common and the non-common points.Furthermore,as the large condition number of the normal matrix resulted in an intractable form,we introduced the bary-centralization technique and a surrogate process for deterministic element of the normal matrix,and proved its benefit for alleviating the condition number.The experimental results show that our approach can obtain the smaller condition number to stabilize the convergence of the interested parameters.Especially,our approach can be implemented for considering the errors of the common and the non-common points,thus the accuracy of the transformed coordinates improves.展开更多
We focus on the single layer formulation which provides an integral equation of the first kind that is very badly conditioned. The condition number of the unpreconditioned system increases exponentially with the multi...We focus on the single layer formulation which provides an integral equation of the first kind that is very badly conditioned. The condition number of the unpreconditioned system increases exponentially with the multiscale levels. A remedy utilizing overlapping domain decompositions applied to the Boundary Element Method by means of wavelets is examined. The width of the overlapping of the subdomains plays an important role in the estimation of the eigenvalues as well as the condition number of the additive domain decomposition operator. We examine the convergence analysis of the domain decomposition method which depends on the wavelet levels and on the size of the subdomain overlaps. Our theoretical results related to the additive Schwarz method are corroborated by numerical outputs.展开更多
It is known in the computational electromagnetics (CEM) that the node element has a relative wellconditioned matrix, but suffers from the spurious solution problem; whereas the edge element has no spurious solutions...It is known in the computational electromagnetics (CEM) that the node element has a relative wellconditioned matrix, but suffers from the spurious solution problem; whereas the edge element has no spurious solutions, but usually produces an ill-conditioned matrix. Particularly, when the mesh is over dense, the iterative solution of the matrix equation from edge element converges very slowly. Based on the node element and edge element, a node-edge element is presented, which has no spurious solutions and better-conditioned matrix. Numerical experiments demonstrate that the proposed node-edge element is more efficient than now-widely used edge element.展开更多
Matrix perturbation theory is utilized to investigate high-rank line of sight multiple input multiple output channels in a microwave relay system. The upper and lower bounds of channel capacity are derived based on sp...Matrix perturbation theory is utilized to investigate high-rank line of sight multiple input multiple output channels in a microwave relay system. The upper and lower bounds of channel capacity are derived based on space time block codes technique and singular values decomposition. A useful constraint for designing LOS MIMO channels is developed by the use of the condition number of the MIMO channel matrix. The theoretical analysis of channel capacity is confirmed by the simulation. The results show that the proposed method is able to give a physical explanation of the high-rank LOS MIMO channel matrix characteristics.展开更多
A novel method based on ant colony optimization (ACO), algorithm for solving the ill-conditioned linear systems of equations is proposed. ACO is a parallelized bionic optimization algorithm which is inspired from th...A novel method based on ant colony optimization (ACO), algorithm for solving the ill-conditioned linear systems of equations is proposed. ACO is a parallelized bionic optimization algorithm which is inspired from the behavior of real ants. ACO algorithm is first introduced, a kind of positive feedback mechanism is adopted in ACO. Then, the solu- tion problem of linear systems of equations was reformulated as an unconstrained optimization problem for solution by an ACID algorithm. Finally, the ACID with other traditional methods is applied to solve a kind of multi-dimensional Hilbert ill-conditioned linear equations. The numerical results demonstrate that ACO is effective, robust and recommendable in solving ill-conditioned linear systems of equations.展开更多
The morbidity problem of the GM(1,1) power model in parameter identification is discussed by using multiple and rotation transformation of vectors. Firstly we consider the morbidity problem of the special matrix and...The morbidity problem of the GM(1,1) power model in parameter identification is discussed by using multiple and rotation transformation of vectors. Firstly we consider the morbidity problem of the special matrix and prove that the condition number of the coefficient matrix is determined by the ratio of lengths and the included angle of the column vector, which could be adjusted by multiple and rotation transformation to turn the matrix to a well-conditioned one. Then partition the corresponding matrix of the GM(1,1) power model in accordance with the column vector and regulate the matrix to a well-conditioned one by multiple and rotation transformation of vectors, which completely solve the instability problem of the GM(1,1) power model. Numerical results show that vector transformation is a new method in studying the stability problem of the GM(1,1) power model.展开更多
In this paper,we give the sensitivity analyses by two approaches for L,D,U in factorization A=LDU of general perturbations in A which sufficiently small in norm. By the matrix vector equation approach,we derive the sh...In this paper,we give the sensitivity analyses by two approaches for L,D,U in factorization A=LDU of general perturbations in A which sufficiently small in norm. By the matrix vector equation approach,we derive the sharp condition number for L,D and U factors .By the matrix equation approach we derive corresponding condition estimates. When A is a symmetric matrix,the corresponding results can be obtained for LDL T factorization.展开更多
A new interpolation algorithm for Head-Related Transfer Function (HRTF) is proposed to realize 3D sound reproduction via headphones in arbitrary spatial direction. HRTFs are modeled as a weighted sum of spherical ha...A new interpolation algorithm for Head-Related Transfer Function (HRTF) is proposed to realize 3D sound reproduction via headphones in arbitrary spatial direction. HRTFs are modeled as a weighted sum of spherical harmonics on a spherical surface. Truncated Singular Value Decomposition (SVD) is adopted to calculate the weights of the model. The truncation number is chosen according to Frobenius norm ratio and the partial condition number. Compared with other interpolated methods, our proposed approach not only is continuous but exploits global information of available directions. The HRTF from any desired direction can be and interpolated results demonstrate that our obtained more accurately and robustly. Reconstructed proposed algorithm acquired better performance.展开更多
Several important properties of a kind of random symplectic matrix used by A. Bunse-Gerstner and V. Mehrmann are studied and the following results are obtained: 1) It can be transformed to Jordan canonical form by ort...Several important properties of a kind of random symplectic matrix used by A. Bunse-Gerstner and V. Mehrmann are studied and the following results are obtained: 1) It can be transformed to Jordan canonical form by orthogonal similar transformation; 2) Its condition number is a constant; 3) The condition number of it is about 2.618.展开更多
To investigate the observability of gimbled inertial navigation system when the base moves on the basis of piece-wise constant system's observability theory and singular value decomposition, the variation of the s...To investigate the observability of gimbled inertial navigation system when the base moves on the basis of piece-wise constant system's observability theory and singular value decomposition, the variation of the singular value in the observability matrix with time is discussed. The simulation results reveal that only if orientation angle is 60° and the flight route is S-figure in initial alignment, the optimal observability is obtained, thus a theoretical foundation for fast and accurate alignment of GINS is provided.展开更多
文摘A condition number is an amplification coefficient due to errors in computing. Thus the theory of condition numbers plays an important role in error analysis. In this paper, following the approach of Rice, condition numbers are defined for factors of some matrix factorizations such as the Cholesky factorization of a symmetric positive definite matrix and QR factorization of a general matrix. The condition numbers are derived by a technique of analytic expansion of the factor dependent on one parameter and matrix-vector equation. Condition numbers of the Cholesky and QR factors are different from the ones previously introduced by other authors, but similar to Chang's results. In Cholesky factorization, corresponding with the condition number of the factor matrix L , K _L is a low bound of Stewart's condition number K .
基金Supported by the National Natural Science Foundation of China(11671060).
文摘In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setting the specific norms and weight parameters, we present the expressions of the structured normwise, mixed, componentwise condition numbers and the corresponding results for unstructured ones. In addition, we investigate the statistical estimation of condition numbers of LDU factorization using the probabilistic spectral norm estimator and the small-sample statistical condition estimation method, and devise three algorithms. Finally, we compare the structured condition numbers with the corresponding unstructured ones in numerical experiments.
基金This paper was supported by the National Natural Science Foundation of China under Grant No.61390513 and 61201225,and National Science and Technology Major Project of China under Grant No.2013ZX03003004,the Natural Science Foundation of Shanghai under Grant No.12ZR1450800,and sponsored by Shanghai Pujiang Program under Grant No.13PJD030.It was also supported by the Fundamental Research Funds for the Central Universities under Grant No.20140767,the Program for Young Excellent Talents in Tongji University under Grant No.2013KJ007,and 'Chen Guang' project supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation under Grant No.13CG18
文摘In Multiple-Input Multiple-Out (MIMO) systems, the user selection algorithm plays an important role in the realization of multiplexing gain. In this paper, an improved Semi-orthogonal User Selection algorithm based on condition number is proposed. Besides, a new MIMO pre- coding scheme is designed. The proposed SUS- CN (SUS with condition number) algorithm outperforms the SUS algorithm for the selection of users with better matrix inversion property, thus a higher information rate for selected user pair is achieved. The designed MIMO precoding matrix brings benefits of the power equality at transmitted terminals, the limited dynamic range of the power over time, and a better power efficiency. The simulation results give the key insights into the im- pact of the different condition number value and users on the sum-rate capacity.
文摘From the formulas of the conjugate gradient, a similarity between a symmetric positive definite (SPD) matrix A and a tridiagonal matrix B is obtained. The elements of the matrix B are determined by the parameters of the conjugate gradient. The computation of eigenvalues of A is then reduced to the case of the tridiagonal matrix B. The approximation of extreme eigenvalues of A can be obtained as a 'by-product' in the computation of the conjugate gradient if a computational cost of O(s) arithmetic operations is added, where s is the number of iterations This computational cost is negligible compared with the conjugate gradient. If the matrix A is not SPD, the approximation of the condition number of A can be obtained from the computation of the conjugate gradient on AT A. Numerical results show that this is a convenient and highly efficient method for computing extreme eigenvalues and the condition number of nonsingular matrices.
基金The work is partially supported by the National Natural Science Foundation of China (No. 11801362).
文摘In this paper,for the regularized Hermitian and skew-Hermitian splitting(RHSS)preconditioner introduced by Bai and Benzi(BIT Numer Math 57:287–311,2017)for the solution of saddle-point linear systems,we analyze the spectral properties of the preconditioned matrix when the regularization matrix is a special Hermitian positive semidefinite matrix which depends on certain parameters.We accurately describe the numbers of eigenvalues clustered at(0,0)and(2,0),if the iteration parameter is close to 0.An estimate about the condition number of the corresponding eigenvector matrix,which partly determines the convergence rate of the RHSS-preconditioned Krylov subspace method,is also studied in this work.
文摘The authors study the generation of matrices with complex entries belonging to some matrix groups, mainly those that are defined by a scalar product space. These matrices have useful applications in quantum mechanical problems and complex control problems. In this work, the authors try to generate matrices such that: (1) the condition number of these types of matrices is controlled and (2) The algorithm used to generate these matrices preserves their structure.
文摘In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.
文摘In the process of initial alignment for a strapdown inertial navigation system (SINS) on a stationary base, the east gyro drift rate is an important factor affecting the alignment accuracy of the azimuth misalignment angle. When the Kalman filtering algorithm is adopted in initial alignment, it yields a constant error in the estimation of the azimuth misalignment angle because the east gyro drift rate cannot be estimated. To improve the alignment accuracy, a novel alignment method on revolving mounting base is proposed. The Kalman filtering algorithm of extending the measured values is studied. The theory of spectral condition number is utilized to analyze the degrees of observability of states. Simulation results show that the estimation accuracy of the azimuth misalignment angle is greatly improved through revolving mounting base, and the proposed method is efficient in initial alignment for a medium accurate SINS.
基金supported by the National Natural Science Foundation of China (Key technology of neural fiber reconstruction based on MRI),No. 60703045
文摘Diffusion tensor MRI (DT-MRI or DTI) is emerging as an important non-invasive technology for elucidating intemal brain structures. It has recently been utilized to diagnose a series of diseases that affect the integrity of neural systems to provide a basis for neuroregenerative studies. Results from the present study suggested that neural tissue is reconstructed with multiple diffusion-weighted gradient directions DTI, which varies from traditional imaging methods that utilize 6 gradient directions. Simultaneously, the diffusion tensor matrix is obtained by multiple linear regressions from an equation of echo signal intensity. The condition number value and standard deviation of fractional anisotropy for each scheme can be used to evaluate image quality. Results demonstrated that increasing gradient direction to some extent resulted in improved effects. Therefore, the traditional 6 and 15 directions should not be considered optimal scan protocols for clinical DTI application. In a scheme with 20 directions, the condition number and standard deviation of fractional anisotropy of the encoding gradients matrix were significantly reduced, and resulted in more clearly and accurately displayed neural tissue. Results demonstrated that the scheme with 20 diffusion gradient directions provided better accuracy of structural renderings and could be an optimal scan protocol for clinical DTI application.
基金supported by Aeronautical Science Foundation of China(Grant No.20081651025)
文摘The existing researches on singularity of parallel mechanism are mostly limited to the property and regularity of singularity locus and there is no further research into the geometric relationship between uncontrolled kinematic screw and parallel mechanism in singularity. A 3UPS-S parallel mechanism is presented which fulfils 3-DOF in rotation. The regularity of nutation angle singularity is analyzed based on the Jacobian matrix, and the singularity surface of 3UPS-S parallel mechanisms is obtained. By applying the concept of reciprocal product in screw theory, the singular kinematic screw is derived when 3UPS-S parallel mechanism is in singularity. The geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism is investigated by using programs in MATLAB. It is revealed that there are two kinds of situation. Firstly, the three limbs of 3UPS-S parallel mechanism intersect the singular kinematic screw in space simultaneously; Secondly, two limbs cross the singular kinematic screw while the third limb parallels with that screw. It is concluded that the nutation angle singularity of 3UPS-S parallel mechanism belongs to the singular linear complexes. This paper sheds light into and clarifies the geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism.
基金supported by the National Natural Science Foundation of China,Nos.41874001 and 41664001Support Program for Outstanding Youth Talents in Jiangxi Province,No.20162BCB23050National Key Research and Development Program,No.2016YFB0501405。
文摘When linearizing three-dimensional(3 D)coordinate similarity transformation model with large rotations,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the problem,a series of conversions are contributed to the 3 D coordinate similarity transformation model in this paper.We deduced a complete solution for the 3 D coordinate similarity transformation at any rotation with the nonlinear adjustment methodology,which involves the errors of the common and the non-common points.Furthermore,as the large condition number of the normal matrix resulted in an intractable form,we introduced the bary-centralization technique and a surrogate process for deterministic element of the normal matrix,and proved its benefit for alleviating the condition number.The experimental results show that our approach can obtain the smaller condition number to stabilize the convergence of the interested parameters.Especially,our approach can be implemented for considering the errors of the common and the non-common points,thus the accuracy of the transformed coordinates improves.
文摘We focus on the single layer formulation which provides an integral equation of the first kind that is very badly conditioned. The condition number of the unpreconditioned system increases exponentially with the multiscale levels. A remedy utilizing overlapping domain decompositions applied to the Boundary Element Method by means of wavelets is examined. The width of the overlapping of the subdomains plays an important role in the estimation of the eigenvalues as well as the condition number of the additive domain decomposition operator. We examine the convergence analysis of the domain decomposition method which depends on the wavelet levels and on the size of the subdomain overlaps. Our theoretical results related to the additive Schwarz method are corroborated by numerical outputs.
文摘It is known in the computational electromagnetics (CEM) that the node element has a relative wellconditioned matrix, but suffers from the spurious solution problem; whereas the edge element has no spurious solutions, but usually produces an ill-conditioned matrix. Particularly, when the mesh is over dense, the iterative solution of the matrix equation from edge element converges very slowly. Based on the node element and edge element, a node-edge element is presented, which has no spurious solutions and better-conditioned matrix. Numerical experiments demonstrate that the proposed node-edge element is more efficient than now-widely used edge element.
基金supported partly by the National Natural Science Foundation of China(60872022)the"973"Program of China(2008CB317109),the Science Foundation of Guangxi Province of China(0991241)the Foundation of Guangxi Key Laboratory of Information and Communication(10903).
文摘Matrix perturbation theory is utilized to investigate high-rank line of sight multiple input multiple output channels in a microwave relay system. The upper and lower bounds of channel capacity are derived based on space time block codes technique and singular values decomposition. A useful constraint for designing LOS MIMO channels is developed by the use of the condition number of the MIMO channel matrix. The theoretical analysis of channel capacity is confirmed by the simulation. The results show that the proposed method is able to give a physical explanation of the high-rank LOS MIMO channel matrix characteristics.
文摘A novel method based on ant colony optimization (ACO), algorithm for solving the ill-conditioned linear systems of equations is proposed. ACO is a parallelized bionic optimization algorithm which is inspired from the behavior of real ants. ACO algorithm is first introduced, a kind of positive feedback mechanism is adopted in ACO. Then, the solu- tion problem of linear systems of equations was reformulated as an unconstrained optimization problem for solution by an ACID algorithm. Finally, the ACID with other traditional methods is applied to solve a kind of multi-dimensional Hilbert ill-conditioned linear equations. The numerical results demonstrate that ACO is effective, robust and recommendable in solving ill-conditioned linear systems of equations.
基金supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China(20120143110001)the General Education Program Requirements in the Humanities and Social Sciences of China(11YJC630155)the Youth Foundation of Hubei Province of China(Q20121203)
文摘The morbidity problem of the GM(1,1) power model in parameter identification is discussed by using multiple and rotation transformation of vectors. Firstly we consider the morbidity problem of the special matrix and prove that the condition number of the coefficient matrix is determined by the ratio of lengths and the included angle of the column vector, which could be adjusted by multiple and rotation transformation to turn the matrix to a well-conditioned one. Then partition the corresponding matrix of the GM(1,1) power model in accordance with the column vector and regulate the matrix to a well-conditioned one by multiple and rotation transformation of vectors, which completely solve the instability problem of the GM(1,1) power model. Numerical results show that vector transformation is a new method in studying the stability problem of the GM(1,1) power model.
基金863 project of China,under grantnumbers86 3-30 6 -ZD0 1 -0 3-2 ,86 3-30 6 -ZD1 1 -0 3-1,by 973project of Chinaundergrant number G1 9990 32 80 3
文摘In this paper,we give the sensitivity analyses by two approaches for L,D,U in factorization A=LDU of general perturbations in A which sufficiently small in norm. By the matrix vector equation approach,we derive the sharp condition number for L,D and U factors .By the matrix equation approach we derive corresponding condition estimates. When A is a symmetric matrix,the corresponding results can be obtained for LDL T factorization.
基金Supported by Shanghai Natural Science Foundation, Shanghai Leading Academic Discipline Project, and STCSM of China (No. 08ZR1408300, S30108, and 08DZ2231100)
文摘A new interpolation algorithm for Head-Related Transfer Function (HRTF) is proposed to realize 3D sound reproduction via headphones in arbitrary spatial direction. HRTFs are modeled as a weighted sum of spherical harmonics on a spherical surface. Truncated Singular Value Decomposition (SVD) is adopted to calculate the weights of the model. The truncation number is chosen according to Frobenius norm ratio and the partial condition number. Compared with other interpolated methods, our proposed approach not only is continuous but exploits global information of available directions. The HRTF from any desired direction can be and interpolated results demonstrate that our obtained more accurately and robustly. Reconstructed proposed algorithm acquired better performance.
文摘Several important properties of a kind of random symplectic matrix used by A. Bunse-Gerstner and V. Mehrmann are studied and the following results are obtained: 1) It can be transformed to Jordan canonical form by orthogonal similar transformation; 2) Its condition number is a constant; 3) The condition number of it is about 2.618.
文摘To investigate the observability of gimbled inertial navigation system when the base moves on the basis of piece-wise constant system's observability theory and singular value decomposition, the variation of the singular value in the observability matrix with time is discussed. The simulation results reveal that only if orientation angle is 60° and the flight route is S-figure in initial alignment, the optimal observability is obtained, thus a theoretical foundation for fast and accurate alignment of GINS is provided.