Factorized Smith Method for A Class of High-Ranked Large-Scale T-Stein Equations  

一类高秩大规模T-Stein方程的分解Smith方法

作　　者：LI Xiang YU Bo TANG Qiong 李想;余波;汤琼

机构地区：[1]School of Science,Hunan University of Technology,Zhuzhou 412007,China

出　　处：《Chinese Quarterly Journal of Mathematics》2024年第3期235-249,共15页数学季刊（英文版）

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).

摘　　要：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.

关 键 词：Large-scale T-Stein equations High-ranked Deflation and shift Partially truncation and compression Smith method 

分 类 号：O241[理学—计算数学]