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I am looking for a reference - paper, book, discussion, anything that has a mathematical proof for stability of the conjugate gradient method in floating point arithmetic.

Something similar for modified Gram-Schmidt would be as good.

Does anyone have any suggestions?

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    $\begingroup$ I presume you've already seen this, this, and this... $\endgroup$ – J. M. Dec 23 '11 at 14:34
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Some more references:

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The Lanczos and Conjugate Gradient algorithms: From Theory to Finite Precision Computations presents a thorough analysis of CG in finite precision arithmetic.

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