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On the Computation of the Matrix k ‐th Root
Author(s) -
Lakić Slobodan
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199803)78:3<167::aid-zamm167>3.0.co;2-r
Subject(s) - root (linguistics) , computation , root finding algorithm , inverse , mathematics , stability (learning theory) , matrix (chemical analysis) , iterative method , computer science , algorithm , geometry , physics , materials science , nonlinear system , philosophy , linguistics , quantum mechanics , machine learning , composite material
In this paper we derive a family of iterative methods for computing the k ‐th root and the inverse k ‐th root of a given matrix. We will show that the methods are locally convergent. The methods are analyzed and their numerical stability is investigated.