Conjugate gradient squared method: Difference between revisions

Revision as of 16:22, 29 December 2023

Revision as of 16:22, 29 December 2023

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{{Short description|Algorithm for solving matrix-vector equations}}

{{Draft topics|mathematics}}

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{{AFC comment|1=Thanks for your submission! I'm going to have to decline this for now as the draft is essentially just a statement of the algorithm with no explanation. This is not useful as an encyclopedic reference, as the [[WP:MTAU|significant technical language]] makes it difficult to read for anyone other than people familiar with the subject. Let me know if you have any questions! <span class="nowrap">—[[User:TechnoSquirrel69|TechnoSquirrel69]]</span> ([[User talk:TechnoSquirrel69|sigh]]) 20:01, 4 November 2023 (UTC)}}

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In [[numerical linear algebra]], the '''conjugate gradient squared method (CGS)''' is an [[iterative method|iterative]] algorithm for solving [[systems of linear equations]] of the form <math>A{\bold x} = {\bold b}</math>, particularly in cases where computing the [[transpose]] <math>A^T</math> is impractical.<ref name="mathworld">{{cite web|title=Conjugate Gradient Squared Method|author1=Noel Black|author2=Shirley Moore|publisher=[[MathWorld|Wolfram Mathworld]]|url=https://mathworld.wolfram.com/ConjugateGradientSquaredMethod.html}}</ref> The CGS method was developed as an improvement to the [[Biconjugate gradient method]].<ref name="matlab">{{cite web|title=cgs|author=[[Mathworks]]|website=[[Matlab]] documentation|url=https://au.mathworks.com/help/matlab/ref/cgs.html}}</ref><ref name="vorst03">{{cite book|author=[[Henk van der Vorst]]|title=Iterative Krylov Methods for Large Linear Systems|chapter=Bi-Conjugate Gradients|year=2003|publisher=Cambridge University Press |isbn=0-521-81828-1}}</ref><ref name="SIAM">{{cite journal|title=CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems|author=Peter Sonneveld|journal=SIAM Journal on Scientific and Statistical Computing|volume=10|issue=1|pages=36–52|date=1989|url=https://www.proquest.com/docview/921988114|url-access=limited|doi=10.1137/0910004|id={{ProQuest|921988114}} }}</ref>

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== References ==

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{{Reflist}}

[[:Category:Numerical linear algebra]]

[[:Category:Gradient methods]]