The proportionate recursive least squares(PRLS)algorithm has shown faster convergence and better performance than both proportionate updating(PU)mechanism based least mean squares(LMS)algorithms and RLS algorithms wit...The proportionate recursive least squares(PRLS)algorithm has shown faster convergence and better performance than both proportionate updating(PU)mechanism based least mean squares(LMS)algorithms and RLS algorithms with a sparse regularization term.In this paper,we propose a variable forgetting factor(VFF)PRLS algorithm with a sparse penalty,e.g.,l_(1)-norm,for sparse identification.To reduce the computation complexity of the proposed algorithm,a fast implementation method based on dichotomous coordinate descent(DCD)algorithm is also derived.Simulation results indicate superior performance of the proposed algorithm.展开更多
In solving application problems, many largesscale nonlinear systems of equations result in sparse Jacobian matrices. Such nonlinear systems are called sparse nonlinear systems. The irregularity of the locations of non...In solving application problems, many largesscale nonlinear systems of equations result in sparse Jacobian matrices. Such nonlinear systems are called sparse nonlinear systems. The irregularity of the locations of nonzero elements of a general sparse matrix makes it very difficult to generally map sparse matrix computations to multiprocessors for parallel processing in a well balanced manner. To overcome this difficulty, we define a new storage scheme for general sparse matrices in this paper. With the new storage scheme, we develop parallel algorithms to solve large-scale general sparse systems of equations by interval Newton/Generalized bisection methods which reliably find all numerical solutions within a given domain.In Section 1, we provide an introduction to the addressed problem and the interval Newton's methods. In Section 2, some currently used storage schemes for sparse sys-terns are reviewed. In Section 3, new index schemes to store general sparse matrices are reported. In Section 4, we present a parallel algorithm to evaluate a general sparse Jarobian matrix. In Section 5, we present a parallel algorithm to solve the correspond-ing interval linear 8ystem by the all-row preconditioned scheme. Conclusions and future work are discussed in Section 6.展开更多
We propose,in this paper,the preconditioned accelerated generalized successive overrelaxation(PAGSOR)iteration method for efficiently solving the large complex symmetric linear systems.To solve the nonlinear systems w...We propose,in this paper,the preconditioned accelerated generalized successive overrelaxation(PAGSOR)iteration method for efficiently solving the large complex symmetric linear systems.To solve the nonlinear systems whose Jacobian matrices are complex and symmetric,treating the PAGSOR method as internal iteration,we construct a modified Newton-PAGSOR(MN-PAGSOR)method to provide an effective approach for solving a wide range of problems in various scientific and engineering fields.Based on the Hölder continuous condition we present the theoretical framework of the modified method,demonstrate its local convergence properties,and provide numerical experiments to validate its effectiveness in solving a class of nonlinear systems.展开更多
This paper presents a highly parallelizable numerical method to solve time dependent acoustic obstacle scattering problems.The method proposed is a generalization of the“operator expansion method”developed by Recchi...This paper presents a highly parallelizable numerical method to solve time dependent acoustic obstacle scattering problems.The method proposed is a generalization of the“operator expansion method”developed by Recchioni and Zirilli[SIAM J.Sci.Comput.,25(2003),1158-1186].The numerical method proposed reduces,via a perturbative approach,the solution of the scattering problem to the solution of a sequence of systems of first kind integral equations.The numerical solution of these systems of integral equations is challenging when scattering problems involving realistic obstacles and small wavelengths are solved.A computational method has been developed to solve these challenging problems with affordable computing resources.To this aim a new way of using the wavelet transform and new bases of wavelets are introduced,and a version of the operator expansion method is developed that constructs directly element by element in a fully parallelizable way.Several numerical experiments involving realistic obstacles and“small”wavelengths are proposed and high dimensional vector spaces are used in the numerical experiments.To evaluate the performance of the proposed algorithm on parallel computing facilities,appropriate speed up factors are introduced and evaluated.展开更多
基金supported by National Key Research and Development Program of China(2020YFB0505803)National Key Research and Development Program of China(2016YFB0501700)。
文摘The proportionate recursive least squares(PRLS)algorithm has shown faster convergence and better performance than both proportionate updating(PU)mechanism based least mean squares(LMS)algorithms and RLS algorithms with a sparse regularization term.In this paper,we propose a variable forgetting factor(VFF)PRLS algorithm with a sparse penalty,e.g.,l_(1)-norm,for sparse identification.To reduce the computation complexity of the proposed algorithm,a fast implementation method based on dichotomous coordinate descent(DCD)algorithm is also derived.Simulation results indicate superior performance of the proposed algorithm.
文摘In solving application problems, many largesscale nonlinear systems of equations result in sparse Jacobian matrices. Such nonlinear systems are called sparse nonlinear systems. The irregularity of the locations of nonzero elements of a general sparse matrix makes it very difficult to generally map sparse matrix computations to multiprocessors for parallel processing in a well balanced manner. To overcome this difficulty, we define a new storage scheme for general sparse matrices in this paper. With the new storage scheme, we develop parallel algorithms to solve large-scale general sparse systems of equations by interval Newton/Generalized bisection methods which reliably find all numerical solutions within a given domain.In Section 1, we provide an introduction to the addressed problem and the interval Newton's methods. In Section 2, some currently used storage schemes for sparse sys-terns are reviewed. In Section 3, new index schemes to store general sparse matrices are reported. In Section 4, we present a parallel algorithm to evaluate a general sparse Jarobian matrix. In Section 5, we present a parallel algorithm to solve the correspond-ing interval linear 8ystem by the all-row preconditioned scheme. Conclusions and future work are discussed in Section 6.
基金National Natural Science Foundation of China with Grant Nos.12161030,12171216.
文摘We propose,in this paper,the preconditioned accelerated generalized successive overrelaxation(PAGSOR)iteration method for efficiently solving the large complex symmetric linear systems.To solve the nonlinear systems whose Jacobian matrices are complex and symmetric,treating the PAGSOR method as internal iteration,we construct a modified Newton-PAGSOR(MN-PAGSOR)method to provide an effective approach for solving a wide range of problems in various scientific and engineering fields.Based on the Hölder continuous condition we present the theoretical framework of the modified method,demonstrate its local convergence properties,and provide numerical experiments to validate its effectiveness in solving a class of nonlinear systems.
文摘This paper presents a highly parallelizable numerical method to solve time dependent acoustic obstacle scattering problems.The method proposed is a generalization of the“operator expansion method”developed by Recchioni and Zirilli[SIAM J.Sci.Comput.,25(2003),1158-1186].The numerical method proposed reduces,via a perturbative approach,the solution of the scattering problem to the solution of a sequence of systems of first kind integral equations.The numerical solution of these systems of integral equations is challenging when scattering problems involving realistic obstacles and small wavelengths are solved.A computational method has been developed to solve these challenging problems with affordable computing resources.To this aim a new way of using the wavelet transform and new bases of wavelets are introduced,and a version of the operator expansion method is developed that constructs directly element by element in a fully parallelizable way.Several numerical experiments involving realistic obstacles and“small”wavelengths are proposed and high dimensional vector spaces are used in the numerical experiments.To evaluate the performance of the proposed algorithm on parallel computing facilities,appropriate speed up factors are introduced and evaluated.
