对称不定系统的一类预处理子的注记

A Note on the Preconditioner for Symmetric Indefinite Systems

由于对称正定系统已有很多有效的求解方法,因此将对称的、或者非对称的不定系统转化为对称正定系统就成为解决这类问题的方法之一构造了一类简洁有效的预处理子,将对称不定系统转化为对称正定型,研究了所得预处理系统的谱性质,估计了其谱条件数,推广了现有结论.

As we know, many methods are very efficient for symmetric and positive definite systems but for symmetric or nonsymmetric indefinite systems from many real applications we are not so lucky. Thus some methods which can transform these systems into symmetric and positive definite systems are presented recently. In this paper an effective preconditioner which transform symmetric indefinite system into symmetric and positive definite system is constructed and presented. The eigenvalue distribution of the preconditioned matrix is determined, as well as the condition number. Some recent results are extended.