Milestones in the Development of Iterative Solution Methods

0353487 - ÚGN 2011 RIV US eng J - Journal Article
Axelsson, Owe
Milestones in the Development of Iterative Solution Methods.
Journal of Electrical and Computer Engineering. Roč. 2010, - (2010), s. 1-33. ISSN 2090-0147
Institutional research plan: CEZ:AV0Z30860518
Keywords : iterative solution methods * convergence acceleration methods * linear systems
Subject RIV: JC - Computer Hardware ; Software
http://www.hindawi.com/journals/jece/2010/972794.html http://arl-repository.lib.cas.cz/uloziste_av/UGN-S/cav_un_epca-0353487_01.pdf

Iterative solution methods to solve linear systems of equations were originally formulated as basic iteration methods of defectcorrection type, commonly referred to as Richardson’s iteration method. These methods developed further into various versions of splitting methods, including the successive overrelaxation (SOR) method.Later, immensely important developments included convergence acceleration methods, such as the Chebyshev and conjugate gradient iteration methods and preconditioning methods of various forms. A major strive has been to find methods with total computational complexity of optimal order, that is, proportional to the degrees of freedom involved in the equation. Methods that we have turned out to have been particularly important for the further developments of linear equation solvers are surveyed. Some if them are presented in greater detail.
Permanent Link: http://hdl.handle.net/11104/0192730