Study of methods of computing transition matrices

Various methods of computing the square matrices ¿ = eAT and ¿ = ¿T0 e A¿ d¿ are studied. They are programmed in FORTRAN and compared for storage, speed and accuracy on a variety of test matrices. The methods studied are power-series expansion and related approximants; the eigenvalue methods of Sylvester´s expansion and diagonal transformation; and numerical integration. The rational approximant to the power-series expansion and a block-diagonal transformation are shown to be the superior methods.