若干Krylov子空间方法及应用比较  

Comparison of Several Krylov Subspace Methods and Their Applications

作　　者：陈晓花 张芳红 陈芳如 CHEN Xiao-hua;ZHANG Fang-hong;CHEN Fang-ru(Department of Mathematics,Lanzhou Technology and Business College,Lanzhou Gansu 730101,China)

机构地区：[1]兰州工商学院大学数学部,甘肃兰州730101

出　　处：《萍乡学院学报》2023年第3期1-6,共6页Journal of Pingxiang University

基　　金：甘肃省教育科学十四五规划课题“民办院校基于应用型人才培养的线性代数分类教学改革与实践”(GS[2021]GHB1806)。

摘　　要：文章首先介绍Krylov子空间方法类算法中最具代表性的几种算法:CGNR算法、GMRES算法、BiCG算法、CGS算法、BiCGSTAB算法及QMR算法等;其次讨论这几种算法之间的关系及各自的优点与不足;最后针对某一类数值算例来验证所得结论的正确性。Several representative algorithms of Krylov subspace are introduced in the paper,such as CGNR algorithm,GMRES algorithm,BiCG algorithm,CGS algorithm,BiCGSTAB algorithm and QMR algorithm.Then the relationships among these algorithms and their advantages and deficiencie are discusssed.Finally,some numerical examples are used to verify the correctness of the conclusions.

关 键 词：KRYLOV子空间 CGNR算法 GMRES算法 双正交Lanczos类算法 

分 类 号：O24[理学—计算数学]