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Normal Hyperbolicity of Manifolds of Equilibria in Nonlinear Circuits with Mem-Devices Read chapter Read first chapter

2014 | OriginalPaper | Chapter

Computing Hyperbolic Matrix Functions Using Orthogonal Matrix Polynomials

Authors : Emilio Defez, Jorge Sastre, Javier Ibáñez, Pedro A. Ruiz

Published in: Progress in Industrial Mathematics at ECMI 2012

Publisher: Springer International Publishing

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Abstract

Hyperbolic matrix functions play a fundamental role in the exact solution of coupled partial differential systems of hyperbolic type. For the numerical solution of these problems, analytic-numerical approximations are most suitable obtained by using the hyperbolic matrix functions sinh(A) and cosh(A). It is well known that the computation of both functions can be reduced to the cosine of a matrix cos(A), which can be effectively calculated, with the disadvantage, however, to require complex arithmetic even though the matrix A is real. In this work we focus on approximate calculation of the hyperbolic matrix cosine cosh(A) using the truncation of a Hermite matrix polynomials series for cosh(A). The proposed approximation allows the efficient computation of this matrix function. An illustrative example is given.

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previous chapter Time-Exact Solution of Large Linear ODE Systems by Block Krylov Subspace Projections
next chapter Counter-Harmonic Mean of Symmetric Positive Definite Matrices: Application to Filtering Tensor-Valued Images
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Metadata
Title
Computing Hyperbolic Matrix Functions Using Orthogonal Matrix Polynomials
Authors
Emilio Defez
Jorge Sastre
Javier Ibáñez
Pedro A. Ruiz
Copyright Year
2014
Book
Progress in Industrial Mathematics at ECMI 2012

Print ISBN: 978-3-319-05364-6

Electronic ISBN: 978-3-319-05365-3

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-05365-3_56

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