When Modified Gram-schmidt Generates a Well-conditioned Set of Vectors

Abstract

Orthogonalization methods play a key role in many iterative methods. In this paper, we establish new properties for the modified Gram-Schmidt algorithm. We show why the modified Gram-Schmidt algorithm generates a well-conditioned set of vectors. This result holds under the assumption that the initial matrix is not “too ill-conditioned” in a way that is… (More)

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