## 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

### Citations:

Zbl 0515.65037; Zbl 0625.65032

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