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arXiv · 1710.03409

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

Long Chen·Yongke Wu
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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 $(\sqrt{5}-1)/2$. Similar convergence result is also obtained for a class of inexact Uzawa method with even weaker contraction bound $\sqrt{2}/2$. Preconditioned generalized minimal residual method using BWY method as a preconditioner is shown to converge with realistic assumptions.

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Long Chen, Yongke Wu. 2017-10-10. Convergence Analysis for A Class of Iterative Methods for Solving Saddle Point Systems. https://arxiv.org/abs/1710.03409

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