On high-order iterative schemes for the matrix pth root avoiding the use of inverses
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Amat Plata, Sergio; Busquier Sáez, Sonia; Hernández Verón, Miguel Ángel; Magreñán Ruiz, Ángel AlbertoKnowledge Area
Matemática AplicadaSponsors
The research of the authors S.A. and S.B. was funded in part by Programa de Apoyo a la investigación de la Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia 20928/PI/18 and by PID2019-108336GB-100 (MINECO/FEDER). The research of the author M.Á.H.-V. was supported in part by Spanish MCINN PGC2018-095896-B-C21. The research of the author Á.A.M. was funded in part by Programa de Apoyo a la investigación de la Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia 20928/PI/18 and by Spanish MCINN PGC2018-095896-B-C21.Publication date
2021Publisher
MDPIBibliographic Citation
Amat, S.; Busquier, S.; Hernández-Verón, M.Á.; Magreñán, Á.A. On High-Order Iterative Schemes for the Matrix pth Root Avoiding the Use of Inverses. Mathematics 2021, 9, 144. https://doi.org/10.3390/math9020144Keywords
Matrix pth rootInverse operator
Iterative method
Order of convergence
Stability
Semilocal convergence
Abstract
This paper is devoted to the approximation of matrix pth 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 pth 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.
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