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2006.181: Computing real square roots of a real matrix

2006.181: Nicholas J. Higham (1987) Computing real square roots of a real matrix. Linear Algebra and its Applications, 88-89. pp. 405-430. ISSN 0024-3795

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DOI: 10.1016/0024-3795(87)90118-2

Abstract

Björck and Hammarling [1] describe a fast, stable Schur method for computing a square root X of a matrix A (X2 = A). We present an extension of their method which enables real arithmetic to be used throughout when computing a real square root of a real matrix. For a nonsingular real matrix A conditions are given for the existence of a real square root, and for the existence of a real square root which is a polynomial in A; the number of square roots of the latter type is determined. The conditioning of matrix square roots is investigated, and an algorithm is given for the computation of a well-conditioned square root.

Item Type:Article
Subjects:MSC 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 65 Numerical analysis
MIMS number:2006.181
Deposited By:Miss Louise Stait
Deposited On:05 July 2006

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