On High-Order Iterative Schemes for the Matrix p th Root Avoiding the Use of Inverses

Sergio Amat, Sonia Busquier, Miguel Ángel Hernández-Verón and Ángel Alberto Magreñán
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Sergio Amat: Department of Applied Mathematics and Statistics, Polytechnic University of Cartagena, 30203 Cartagena, Spain
Sonia Busquier: Department of Applied Mathematics and Statistics, Polytechnic University of Cartagena, 30203 Cartagena, Spain
Miguel Ángel Hernández-Verón: Department of Mathematics and Computation, University of La Rioja, 26006 Logroño, Spain
Ángel Alberto Magreñán: Department of Mathematics and Computation, University of La Rioja, 26006 Logroño, Spain

Mathematics, 2021, vol. 9, issue 2, 1-8

Abstract: This paper is devoted to the approximation of matrix p th roots. We present and analyze a family of algorithms free of inverses. The method is a combination of two families of iterative methods. The first one gives an approximation of the matrix inverse. The second family computes, using the first method, an approximation of the matrix p th root. We analyze the computational cost and the convergence of this family of methods. Finally, we introduce several numerical examples in order to check the performance of this combination of schemes. We conclude that the method without inverse emerges as a good alternative since a similar numerical behavior with smaller computational cost is obtained.

Keywords: matrix p th root; inverse operator; iterative method; order of convergence; stability; semilocal convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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