GMRES implementations and residual smoothing techniques for solving ill-posed linear systems

Authors:
M. Matinfar;H. Zareamoghaddam;M. Eslami;M. Saeidy
Affiliations:
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran;Young Researchers Club, Kashmar branch, Islamic Azad University, Kashmar, Iran;Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran;Nour branch, Islamic Azad University, Nour, Iran
Venue:
Computers & Mathematics with Applications
Year:
2012

Citing 16
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Abstract

There are verities of useful Krylov subspace methods to solve nonsymmetric linear system of equations. GMRES is one of the best Krylov solvers with several different variants to solve large sparse linear systems. Any GMRES implementation has some advantages. As the solution of ill-posed problems are important. In this paper, some GMRES variants are discussed and applied to solve these kinds of problems. Residual smoothing techniques are efficient ways to accelerate the convergence speed of some iterative methods like CG variants. At the end of this paper, some residual smoothing techniques are applied for different GMRES methods to test the influence of these techniques on GMRES implementations.