Study of methods of computing transition matrices

Various methods of computing the square matrices φ = eAT and θ = ∫T0 e Aτ dτ 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.