We introduce a factorized Smith method(FSM)for solving large-scale highranked T-Stein equations within the banded-plus-low-rank structure framework.To effectively reduce both computational complexity and storage requi...We introduce a factorized Smith method(FSM)for solving large-scale highranked T-Stein equations within the banded-plus-low-rank structure framework.To effectively reduce both computational complexity and storage requirements,we develop techniques including deflation and shift,partial truncation and compression,as well as redesign the residual computation and termination condition.Numerical examples demonstrate that the FSM outperforms the Smith method implemented with a hierarchical HODLR structured toolkit in terms of CPU time.展开更多
This paper deals with the numerical solution of the large-scale Stein and discrete-time Lyapunov matrix equations.Based on the global Arnoldi process and the squared Smith iteration,we propose a low-rank global Krylov...This paper deals with the numerical solution of the large-scale Stein and discrete-time Lyapunov matrix equations.Based on the global Arnoldi process and the squared Smith iteration,we propose a low-rank global Krylov squared Smith method for solving large-scale Stein and discrete-time Lyapunov matrix equations,and estimate the upper bound of the error and the residual of the approximate solutions for the matrix equations.Moreover,we discuss the restarting of the low-rank global Krylov squared Smith method and provide some numerical experiments to show the efficiency of the proposed method.展开更多
基金Supported partly by NSF of China(Grant No.11801163)NSF of Hunan Province(Grant Nos.2021JJ50032,2023JJ50164 and 2023JJ50165)Degree&Postgraduate Reform Project of Hunan University of Technology and Hunan Province(Grant Nos.JGYB23009 and 2024JGYB210).
文摘We introduce a factorized Smith method(FSM)for solving large-scale highranked T-Stein equations within the banded-plus-low-rank structure framework.To effectively reduce both computational complexity and storage requirements,we develop techniques including deflation and shift,partial truncation and compression,as well as redesign the residual computation and termination condition.Numerical examples demonstrate that the FSM outperforms the Smith method implemented with a hierarchical HODLR structured toolkit in terms of CPU time.
基金supported by the National Natural Science Foundation of China under grant No.11571171.
文摘This paper deals with the numerical solution of the large-scale Stein and discrete-time Lyapunov matrix equations.Based on the global Arnoldi process and the squared Smith iteration,we propose a low-rank global Krylov squared Smith method for solving large-scale Stein and discrete-time Lyapunov matrix equations,and estimate the upper bound of the error and the residual of the approximate solutions for the matrix equations.Moreover,we discuss the restarting of the low-rank global Krylov squared Smith method and provide some numerical experiments to show the efficiency of the proposed method.
