Convergence Analysis for a Class of Iterative Methods for Solving Saddle Point Systems
نویسندگان
چکیده
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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