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A Schur algorithm for computing matrix \(p\)th roots. (English) Zbl 1040.65038

The paper deals with computing matrix \(p\)th roots. Newton’s method for solving the matrix \(p\)th root problem is studied. It is shown that Newton’s method is usually unstable. Then, a Schur method for computing the matrix \(p\)th root is presented. This algorithm is a generalization of the algorithms for computing square roots of a matrix proposed by A. Björck and S. Hammarling [Linear Algebra Appl. 52/53, 127–140 (1983; Zbl 0515.65037)] and N. J. Higham [Linear Algebra Appl. 88/89, 405–430 (1987; Zbl 0625.65032)]. The rounding error analysis given shows that the presented Schur algorithm is numerically stable.

MSC:

65F30 Other matrix algorithms (MSC2010)
15A24 Matrix equations and identities

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