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:<math>\boldsymbol{Ax}=\boldsymbol{b}</math>
where <math>\boldsymbol{A}</math> is [[Symmetric matrix|symmetric]] [[Positive-definite matrix|positive-definite]]. The conjugate gradient method can be derived from several different perspectives, including specialization of the [[conjugate direction method]]<ref>Conjugate Direction Methods http://user.it.uu.se/~matsh/opt/f8/node5.html</ref> for [[Optimization (mathematics)|optimization]], and variation of the [[Arnoldi iteration|Arnoldi]]/[[Lanczos iteration|Lanczos]] iteration for [[eigenvalue]] problems.
The intent of this article is to document the important steps in these derivations.
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