Suppose that we have a unknown vector norm but there is a machine that get a vector and correctly tell us the norm of the vector. Is there any algorithm to compute the matrix norm corresponding to this vector norm? Thanks for any help.
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Your question is more general, but this question and the answers are relevant to your question http://math.stackexchange.com/questions/37913/how-do-i-calculate-the-p-norm-of-a-matrix – Carl Christian Jun 01 '16 at 08:37
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I would guess you have in mind the operator norm of a square matrix corresponding to the (unknown but computable) vector norm, i.e. $$\sup_{v\neq 0} \frac{||Av||}{||v||}$$ – hardmath Jun 02 '16 at 12:21