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==Conjugate Gradient method is not derived here==
This is not a derivation at all. This just lists what to do to do this method.
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:Like it or nor, if you bother to read their ground-breaking paper at all, you will see that this ''is'' the published way Hestenes and Stiefel developed CG. Hestenes and Stiefel introduced the function <math>f(\boldsymbol{x})</math> to show how the conjugate directions method can be viewed as a relaxation method. That function so happens to induce successive minima along the search directions that correspond to the iterates of CG. This could well be a coincidence, whose origin you simply cannot question. Some more common sense tells you that this section is unfinished. Hestenes and Stiefel devoted an entire section in their paper to deriving CG from CD, which just cannot be squeezed into this few words. [[User:Kxx|Kxx]] ([[User talk:Kxx|talk]] | [[Special:Contributions/Kxx|contribs]]) 08:20, 1 February 2011 (UTC)
::Like it not, that is *not* the function Hestenes and Stiefel minimize. They minimize f(x)=(x-h)^T A (x-h) (or rather f(x)=(x-h,A(x-h), which is the same), where in there notation h is the true solution of Ax=k, i.e. h=A^{-1} k. Then they write it as f(x)=x^T A x-2 h^T x (or rather (x,Ax)-2(x,k)+(h,k), which again is the same omitting some irrelevant constant). I corrected the article to use the second form and replaced h by b for the right hand side, which is more common nowadays. (ezander) [[Special:Contributions/134.169.77.186|134.169.77.186]] ([[User talk:134.169.77.186|talk]]) 17:07, 3 February 2011 (UTC)
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