关于具优势对称部分的不定线性代数方程组的分裂极小残量算法

• 作者: 仇寿霞 白中治
• 来源期刊: 计算数学
• 学科: 数学
• 关键词: 线性代数方程组 不定线性方程组 内外迭代法 子空间迭代法 预处理 收敛性质
• 年，卷（期）: 2002,（1）
• 页码范围: 113-128
• 页数: 16页
• 分类号: O24
• 字数: 8561字
• 语种: 中文
• DOI: 10.3321/j.issn:0254-7791.2002.01.012

摘要

For large sparse system of linear equations with the coefficient matrix with a dominant indefinite symmetric part, we present a class of splitting minimal residual method, briefly called as SMINRES-method, by making use of the inner/outer iteration technique. The SMINRES-method is established by first transforming the linear system into an equivalent fixed-point problem based on the symmetric/skewsymmetric splitting of the coefficient matrix, and then utilizing the minimal residual (MINRES) method as the inner iterate process to get a new approximationto the original system of linear equations at each of the outer iteration step. The MINRES can be replaced by a preconditioned MINRES (PMINRES) at the inner iterate of the SMINRES method, which resulting in the so-called preconditioned splitting minimal residual (PSMINRES) method. Under suitable conditions, we prove the convergence and derive the residual estimates of the new SMINRES and PSMINRES methods. Computations show that numerical behaviours of the SMIN-RES as well as its symmetric Gauss-Seidel (SCS) iteration preconditioned variant,SGS-SMINRES, are superior to those of some standard Krylov subspace methods such as CGS, GMRES and their unsymmetric Gauss-Seidel (UGS) iteration preconditioned variants UGS-CGS and UGS-GMRES.

作者信息

序号	姓名	单位	发文数	被引次数	H指数	G指数
1	白中治	中国科学院数学与系统科学研究院计算数学与科学工程计算研究所科学与工程计算国家重点实验室	6	147	4.0	6.0
2	仇寿霞	中国科学院数学与系统科学研究院计算数学与科学工程计算研究所科学与工程计算国家重点实验室	1	12	1.0	1.0