块对称三对角不定线性系统的预处理方法

On Preconditioners for Block Tridiagonal Symmetric Indefinite Linear Systems

本文研究一类块对称三对角不定系统的预处理技术。把鞍点问题的一种矩阵分解方法推广至块对称三对角不定系统。文中研究了这类矩阵的广义Cholesky分解,利用这种矩阵分解法构造预条件矩阵,证明了新的预条件矩阵使线性方程组具有更小的条件数。最后利用数值算例验证了新给数值方法的有效性。

We discuss a class of preconditioning methods for an iterative solution of block tridiagonal symmetric indefinite linear systems.A kind of matrix decomposition method of saddle point problem is generalized to block tridiagonal symmetric indefinite linear systems.It makes a research on generalized Cholesky decomposition of block tridiagonal symmetric indefinite linear systems in this paper as well as preconditioners are designed in this way.The new preconditioners make a smaller condition number of linear equations.Finally,a numerical example is presented to illustrate the effectiveness of the proposed approach.