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Matrix nearness problems and applications. (English) Zbl 0681.65029
Applications of matrix theory, Proc. Conf., Bradford/UK 1988, Inst. Math. Appl. Conf. Ser., New. Ser. 22, 1-27 (1989).

[For the entire collection see Zbl 0676.00007.]

The following matrix nearness problems are surveyed: finding the nearest symmetric matrix, the nearest positive definite, the orthogonal Procrustes problem (a product formulation of the nearest orthogonal), the nearest normal matrix, and finding the smallest perturbation that makes the matrix unstable. Nearness is measured with either the Frobenius or the spectral norm, and both mathematical characterizations and algorithms are described as well as contexts when the solution of a nearness problem is of interest.

Reviewer: A.Ruhe
MSC:
65F35Matrix norms, conditioning, scaling (numerical linear algebra)
15A60Applications of functional analysis to matrix theory