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What is a good way to check if the any numerical error is occured in conjugate gradient algorithm. Additionally why is it not suggested to check error by checking A-orthogonality of search direction or checking orthogonality of residuals?

Note: here by error I mean error from floating point unit of CPU. In some cases the errors can be due incorrect computation of matrix vector product (in cases where matrix A is not explicitly available).

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For discussion: look at this scicomp.stackexchange.com/questions/4761/… – zimbra314 Nov 28 '12 at 21:15

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