Computation of the cosine of a matrix

This thesis concerns the computation of the cosine of a matrix. To approximate the matrix cosine various approaches involving matrix series, matrix characteristic polynomials, differential equations, matrix eigenvalues and matrix decomposition are described. In particular, we develop the double angle method and discuss the effectiveness of this technique when applied to certain approximation schemes. Computations are done primarily with three algorithms, those being in the form of rational approximants or truncated Taylor series. Further, we deal with a method developed by B. N. Parlett to calculate the functions of a matrix. It is of interest to us to see how the double angle method compares with Parlett's method. Results of our experiments are presented and analyzed.