计算数学
計算數學
계산수학
MATHEMATICA NUMERICA SINICA
2002年
1期
113-128
,共16页
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
線性代數方程組%不定線性方程組%內外迭代法%子空間迭代法%預處理%收斂性質
선성대수방정조%불정선성방정조%내외질대법%자공간질대법%예처리%수렴성질
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.
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.
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.
