关于不定线性方程组的若干预处理子的注记

A Note on some Preconditioners for Indefinite Linear Systems

利用Schur分解,提出KKT型实不定线性系统的若干预处理子,讨论了这些预处理情形下的Krylov子空间方法收敛所需的迭代步数,从而说明这些预处理方法是非常有效的.

Some preconditioners are presented for nonsingular indefinite matrices of saddle-point （or KKT） form on the base of Schur complement, which yields preconditioned matrices with at most 4 distinct eigenvalues （i. e. precisely with minimum polynomial of degree at most 4）. The number of iterations required for convergence of some Krylov subspace methods can be derived. The results show that the preconditioners are very effective.