Sastre, J. (2018). Efficient evaluation of matrix polynomials. Linear Algebra and its Applications. 539:229-250. https://doi.org/10.1016/j.laa.2017.11.010
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/125088
Title:
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Efficient evaluation of matrix polynomials
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Author:
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Sastre, Jorge
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UPV Unit:
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Universitat Politècnica de València. Departamento de Comunicaciones - Departament de Comunicacions
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Issued date:
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Abstract:
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[EN] This paper presents a new family of methods for evaluating matrix polynomials more efficiently than the state-of-the-art Paterson-Stockmeyer method. Examples of the application of the methods to the Taylor polynomial ...[+]
[EN] This paper presents a new family of methods for evaluating matrix polynomials more efficiently than the state-of-the-art Paterson-Stockmeyer method. Examples of the application of the methods to the Taylor polynomial approximation of matrix functions like the matrix exponential and matrix cosine are given. Their efficiency is compared with that of the best existing evaluation schemes for general polynomial and rational approximations, and also with a recent method based on mixed rational and polynomial approximants. For many years, the Paterson-Stockmeyer method has been considered the most efficient general method for the evaluation of matrix polynomials. In this paper we show that this statement is no longer true. Moreover, for many years rational approximations have been considered more efficient than polynomial approximations, although recently it has been shown that often this is not the case in the computation of the matrix exponential and matrix cosine. In this paper we show that in fact polynomial approximations provide a higher order of approximation than the state-of-the-art computational methods for rational approximations for the same cost in terms of matrix products. (C) 2017 Elsevier Inc. All rights reserved.
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Subjects:
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Matrix
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Polynomial
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Rational
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Mixed rational and polynomial
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Approximation
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Computation
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Matrix function
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Copyrigths:
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Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
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Source:
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Linear Algebra and its Applications. (issn:
0024-3795
)
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DOI:
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10.1016/j.laa.2017.11.010
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Publisher:
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Elsevier
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Publisher version:
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http://doi.org/10.1016/j.laa.2017.11.010
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Project ID:
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MINECO/TIN2014-59294-P
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Thanks:
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This work has been supported by Spanish Ministerio de Economia y Competitividad and European Regional Development Fund (ERDF) grant TIN2014-59294-P. We thank the anonymous referee who revised this paper so thoroughly and ...[+]
This work has been supported by Spanish Ministerio de Economia y Competitividad and European Regional Development Fund (ERDF) grant TIN2014-59294-P. We thank the anonymous referee who revised this paper so thoroughly and carefully.
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Type:
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Artículo
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