Efficient and accurate algorithms for computing matrix trigonometric functions

Computation of matrix trigonometric functions has received remarkable attention in thelast decades due to its usefulness in the solution of systems of second order linear differ-ential equations. Moreover, in many cases, the resolution of these systems involves largematrices. So, the use of not only accurate, but also efficient parallel algorithms becomesabsolutely necessary. The more usual methods proposed for computation of trigonometricmatrix functions, see [1], are based on the Padé rational approximantions [2] and Hermitematrix polynomials series expansions [3].In this work, accurate and efficient algorithms based on Taylor matrix expansion for com-puting matrix trigonometric functions sine and cosine are given. A sequential and parallelalgorithms have been developed and compared with the state-of-the-art algorithms for com-puting these matrix functions. References[1] Ch. Tsitouras, V.N. Katsikis, Bounds for Variable Degree Rational L∞ Approxima-tions to the Matrix Cosine, 2014. (http://users.ntua.gr/tsitoura/tsit kats v3.pdf) [2] G.I. Hargreaves, N.J. Higham, Efficient algorithms for the matrix cosine and sine,Numerical Algorithms 40 (2005) 383–400. [3] E. Defez, J. Sastre, J. Ibáñez, P. Ruiz, Computing matrix functions arising in en-gineering models with orthogonal matrix polynomials. Mathematical and ComputerModelling 57 (2013) 1738-1743.