Talk:Derivation of the conjugate gradient method: Difference between revisions

Revision as of 16:54, 31 January 2011

Revision as of 08:20, 1 February 2011

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The derivation should lead to this equation, and also lead to the expressions for alpha and p. Also, why is it that you want to minimize this function? What does this function represent that the entire method is based on minimizing this function? After reading a derivation, it should be clear where all this comes from. This is like saying, 'this is what works, therefore it is derived.'

[[User:Leftynm|Leftynm]] ([[User talk:Leftynm|talk]]) 16:54, 31 January 2011 (UTC)

: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)