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Consider an algorithm for the problem of computing the (full) SVD of a matrix. The data for this problem is a matrix A, and the solution is three matrices U( unitary ), Σ( diagonal ), and V( unitary ) such that A= U ΣV^* . (We are speaking here of explicit matrices U and V, not implicit representations as products of reflectors.) (a) Explain what it would mean for this algorithm to be backward stable. (b) In fact, for a simple reason, this algorithm cannot be backward stable. Explain. (c) Fortun
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