Accelerating the HS-type Richardson Iteration Method with Anderson Mixing  

作　　者：Zhi Zhi LI Huai ZHANG Le OU-YANG 

机构地区：[1]Key Laboratory of Computational Geodynamics,University of Chinese Academy of Sciences,Beijing 100049,P.R.China [2]Guangdong Key Laboratory of Intelligent Information Processing,Shenzhen Key Laboratory of Media Security,and Guangdong Laboratory of Artificial Intelligence and Digital Economy(SZ),College of Electronics and Information Engineering,Shenzhen University,Shenzhen 518060,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第11期2069-2089,共21页数学学报（英文版）

基　　金：Supported by National Science Foundation of China(Grant Nos.41725017 and 42004085);Guangdong Basic and Applied Basic Research Foundation(Grant No.2019A1515110184);the National Key R&D Program of the Ministry of Science and Technology of China(Grant Nos.2020YFA0713400 and 2020YFA0713401)。

摘　　要：The Accelerated Hermitian/skew-Hermitian type Richardson(AHSR)iteration methods are presented for solving non-Hermitian positive definite linear systems with three schemes,by using Anderson mixing.The upper bounds of spectral radii of iteration matrices are studied,and then the convergence theories of the AHSR iteration methods are established.Furthermore,the optimal iteration parameters are provided,which can be computed exactly.In addition,the application to the model convection-diffusion equation is depicted and numerical experiments are conducted to exhibit the effectiveness and confirm the theoretical analysis of the AHSR iteration methods.

关 键 词：Anderson mixing Hermitian/skew-Hermitian splitting the Richardson iteration convergence analyses optimal parameters the model convection-diffusion equation 

分 类 号：O241.6[理学—计算数学]