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Iterative methods for computing the matrix square root

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Abstract

This paper is devoted to the approximation of the square root of a matrix. We present a family of any order of convergence as a generalization of the classical Newton and Chebychev methods. The semilocal convergence of the family is presented. After an analysis of the efficiency, we conclude that the most efficient method depends on the matrix and on the implementation way.

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Acknowledgments

This work has been partially supported by the project MTM2014-52016-C2-1-P of Spanish Ministry of Economy and Competitiveness.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Paseo Alfonso XIII, 52, 30203, Cartagena, Spain

    S. Amat

  2. Department of Mathematics and Computation, University of La Rioja, C/Luis de Ulloa s/n, 26004, Logroño, Spain

    J. A. Ezquerro & M. A. Hernández-Verón

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  1. S. Amat
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  2. J. A. Ezquerro
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  3. M. A. Hernández-Verón
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Correspondence to J. A. Ezquerro.

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Amat, S., Ezquerro, J.A. & Hernández-Verón, M.A. Iterative methods for computing the matrix square root. SeMA 70, 11–21 (2015). https://doi.org/10.1007/s40324-015-0038-9

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  • DOI: https://doi.org/10.1007/s40324-015-0038-9

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