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A note on preconditioned GMRES for solving singular linear systems. (English) Zbl 1186.65040
Summary: For solving a singular linear system \(Ax=b\) by the generalized minimal residual (GMRES) method, it is shown in the literature that if \(A\) is range-symmetric, then GMRES converges safely to a solution. In this paper we consider preconditioned GMRES for solving a singular linear system, we construct preconditioners by so-called proper splittings, which can ensure that the coefficient matrix of the preconditioned system is range-symmetric.
Reviewer: Reviewer (Berlin)

MSC:
65F10 Iterative numerical methods for linear systems
65F08 Preconditioners for iterative methods
Software:
DGMRES
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