A Framework for Generalized Conjugate Gradient Methods - with Special Emphasis on Contributions by Rüdiger Weiss

0404264 - UIVT-O 20020013 RIV NL eng J - Journal Article
Gutknecht, M. H. - Rozložník, Miroslav
A Framework for Generalized Conjugate Gradient Methods - with Special Emphasis on Contributions by Rüdiger Weiss.
Applied Numerical Mathematics. Roč. 41, - (2002), s. 7-22. ISSN 0168-9274. E-ISSN 1873-5460
R&D Projects: GA AV ČR IAA1030103; GA ČR GA101/00/1035
Institutional research plan: AV0Z1030915
Keywords : sparse linear systems * Krylov space method * orthogonal residual method * minimal residual method * conjugate gradient method * residual smoothing * CG * CGNE * CGNR * CR * FOM * GMRES * PRES
Subject RIV: BA - General Mathematics
Impact factor: 0.504, year: 2002

We discuss a general framework for generalized conjugate gradient methods, that is, iterative methods (for solving linear systems) that are based on generating residuals that are formally orthogonal to each other with respect to some true or formal inner product. This includes methods that generate residuals that are minimal with respect to some norm based on an inner product. A similar, even more general framework was introduced and extensively discussed by Weiss in his work. Weiss also emphasized...
Permanent Link: http://hdl.handle.net/11104/0124527