Numerical Computation of Matrix Sign Function by Double Exponential Formula

Abstract

Abstract. The matrix sign function is a matrix function that can be used to solve the Sylvester equation, and algorithms such as the Schur method and the Newton method have been considered as numerical methods for it. In this paper, we propose a method to compute matrix sign functions numerically with Double Exponential (DE) formula, and evaluate its performance theoretically. The proposed method can be applied to large matrices which are difficult to compute by conventional methods by using parallel computation.