ABSTRACT

It is shown in this paper that the Schur complements and the diagonal-Schur complements of DZ-type matrices are DZ-type matrices under some conditions. A numerical example for solving the linear equations with the coefficient matrix being a DZ-type matrix is given to show that the Schur-based Gauss–Seidel iteration method and the Schur-based conjugate gradient method can compute out the solution faster.

中文翻译：

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关于Dashnic–Zusmanovich型矩阵的Schur补

摘要

本文表明，在一定条件下，DZ型矩阵的Schur补和对角Schur补码是DZ型矩阵。给出了一个以系数矩阵为DZ型矩阵求解线性方程组的数值例子，结果表明基于Schur的Gauss-Seidel迭代法和基于Schur的共轭梯度法可以更快地求解。