Approximation of Exponential Function of a Matrix by Continued Fraction Expansion

  • Masatake Mori

    Tokyo Denki University, Japan

Abstract

A numerical method for high order approximation of , where is an matrix and is an  dimensional vector, based on the continued fraction expansion of is given. The approximants of the continued fraction expansion of are shown to satisfy for , which results in an unconditionally stable method when every eigenvalue of lies in the left half-plane or on the imaginary axis.

Cite this article

Masatake Mori, Approximation of Exponential Function of a Matrix by Continued Fraction Expansion. Publ. Res. Inst. Math. Sci. 10 (1974), no. 1, pp. 257–269

DOI 10.2977/PRIMS/1195192181