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{{AfC topic|stem}}
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>Ax = b</math>, particularly in cases where computing the [[transpose]] <math>A^T</math> is impractical.<ref>{{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>{{cite web|title=cgs|author=Mathworks|url=https://au.mathworks.com/help/matlab/ref/cgs.html}}</ref><ref>{{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>{{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>
As with other methods for solving matrix-vector equations, the CGS method can be used to solve optimisation problems
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