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Some properties of range restricted GMRES methods. (English) Zbl 1321.65046
Summary: The generalized minimal residual (GMRES) method is one of the most popular iterative schemes for the solution of large linear systems of equations with a square nonsingular matrix. GMRES-type methods also have been applied to the solution of linear discrete ill-posed problems. Computational experience indicates that for the latter problems variants of the standard GMRES method, that require the solution to live in the range of a positive power of the matrix of the linear system of equations to be solved, generally yield more accurate approximations of the desired solution than standard GMRES. This paper investigates properties of these variants of GMRES.

65F10 Iterative numerical methods for linear systems
65F22 Ill-posedness and regularization problems in numerical linear algebra
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