Convergence Analysis for A Class of Iterative Methods for Solving Saddle Point Systems

2017/10/10 by Chen, Long, Wu, Yongke · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1710.03409

Abstract

Convergence analysis of a nested iterative scheme proposed by Bank,Welfert and Yserentant (BWY) ([Numer. Math., 666: 645-666, 1990]) for solving saddle point system is presented. It is shown that this scheme converges under weaker conditions: the contraction rate for solving the (1,1) block matrix is bound by (√(5)-1)/2. Similar convergence result is also obtained for a class of inexact Uzawa method with even weaker contraction bound √(2)/2. Preconditioned generalized minimal residual method using BWY method as a preconditioner is shown to converge with realistic assumptions.

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