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Iterative algorithms for Gram-Schmidt orthogonalization. (English) Zbl 0667.65037
A Gram-Schmidt algorithm to orthogonalize a sequence of vectors, where one vector at a time is orthogonalized to the set of already orthogonalized vectors is investigated. It is shown that if a reorthogonalization is performed whenever the norm of the vector is decreased more than a certain threshold, a prescribed accuracy of the whole sequence will be obtained both for the classical and the modified variants of the Gram-Schmidt algorithm.
Reviewer: A.Ruhe

MSC:
65F25 Orthogonalization in numerical linear algebra
65G50 Roundoff error
15A23 Factorization of matrices
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