Some properties of range restricted GMRES methods

• M. Bellalij ^[3] ; L. Reichel ^[1] ; H. Sadok ^[2]
  1. [1] Kent State University

     Kent State University

     City of Kent, Estados Unidos

     
  2. [2] University of the Littoral Opal Coast

     University of the Littoral Opal Coast

     Arrondissement de Dunkerque, Francia

     
  3. [3] Université de Valenciennes, France

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• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 290, Nº 1, 2015, págs. 310-318
• Idioma: inglés
• DOI: 10.1016/j.cam.2015.05.008
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• Resumen

  • 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 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.