International Conference on Scientific Computation and Differential Equations

# Invited Talk

### Rational $L_{\infty}$ approximations to the matrix cosine

I. Famelis, C. Tsitouras and V. Katsikis

Abstract
In applications, many processes are described by second order differential equations and the exact solution for these equations is given in terms of the matrix functions sine and cosine. Among the most competitive algorithms for computing these functions are Padé approximations [1]. Here we focus on two classes of matrices, positive and Hermitian. We present intervals of applications for rational $L_{\infty}$ approximations of various degrees and tolerances for these types of matrices in the lines of [2].
Acknowledgements: This research has been co-financed by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) - Research Funding Program: ARCHIMEDES III. Investing in knowledge society through the European Social Fund.

Bibliography
[1] N.J. Higham and M.I. Smith, Computing the matrix cosine, Numer. Algorithms, 34 (2003) 13-26.
[2] G.I. Hargreaves and N.J. Higham, Efficient algorithms for the matrix cosine and sine, Numer. Algorithms 40 (2005) 383-400.

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