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Why is checking orthogonality is not a good way to check Checking for error in conjugate gradient algorithm

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Why is checking orthogonality is not a good way to check for error in conjugate gradient algorithm

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).