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An analysis on the efficiency of Euler’s method for computing the matrix \(p\)th root. (English) Zbl 1424.65062
Summary: It is shown that the matrix sequence generated by Euler’s method starting from the identity matrix converges to the principal \(p\)th root of a square matrix, if all the eigenvalues of the matrix are in a region including the one for Newton’s method given by C.-H. Guo in 2010 [Linear Algebra Appl. 432, No. 8, 1905–1922 (2010; Zbl 1190.65065)]. The convergence is cubic if the matrix is invertible. A modification version of Euler’s method using the Schur decomposition is developed. Numerical experiments show that the modified algorithm has the overall good numerical behavior.

MSC:
65F60 Numerical computation of matrix exponential and similar matrix functions
Software:
Matlab
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