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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>Ax = b</math>, particularly in cases where calculating <math>A^T</math> is impractical.<ref>{{cite web|title=Conjugate Gradient Squared Method|author=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|isbn=0-521-81828-1}}</ref>
== The Algorithm ==
The algorithm is thus:
# Choose an initial guess <math>x_0</math>
# Compute the residual <math>r_0 = b - Ax_0</math>
# Choose another residual <math>\tilde r_0 = r_0</math>
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== See Also ==
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