منابع مشابه
GMRESR: a family of nested GMRES methods
Recently Eirola and Nevanlinna have proposed an iterative solution method for unsymmetric linear systems, in which the preconditioner is updated from step to step. Following their ideas we suggest variants of GMRES, in which a preconditioner is constructed at each iteration step by a suitable approximation process, e.g., by GMRES itself.
متن کاملA comparison of some GMRES-like methods
GMRES and CGS are well-known iterative methods for the solution of certain sparse linear systems with a non-symmetric matrix. These methods have been compared experimentally in many studies and speciic observations on their convergence behaviour have been reported. A new iterative method to solve a non-symmetric system is proposed by Eirola and Nevanlinna. The purpose of this paper is to invest...
متن کاملAugmented GMRES-type methods
GMRES is a popular iterative method for the solution of large linear systems of equations with a square nonsymmetric matrix. The method generates a Krylov subspace in which an approximate solution is determined. We present modifications of the GMRES and the closely related RRGMRES methods that allow augmentation of the Krylov subspaces generated by these methods by a user-supplied subspace. We ...
متن کاملSome properties of range restricted GMRES methods
The 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 ...
متن کاملGmres-type Methods for Inconsistent Systems
Throughout this paper the integer l is defined by (1.3). Saad and Schulz [6, Proposition 2] show that when A is nonsingular and m ≥ l, the solution xm of the minimization problem (1.2) solves the linear system (1.1). The GMRES method is often implemented by first computing an orthogonal basis {vj} min{m,l} j=1 of the Krylov subspace Km(A, r0) by Arnoldi’s method; see Saad [7] or Saad and Schult...
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ژورنال
عنوان ژورنال: Numerical Linear Algebra with Applications
سال: 1994
ISSN: 1070-5325,1099-1506
DOI: 10.1002/nla.1680010404