Improvements and Performance Evaluation of an Algorithm for Computing the Matrix Sign Function Based on the Double-Exponential Integration Formula

Abstract

Abstract. The matrix sign function has applications to the solution of the algebraic Riccati equation and to the computation of matrix eigenvalues. Recently, a new numerical algorithm for the matrix sign function based on the double-exponential integration formula has been proposed and has attracted attention due to its large-grain parallelism. In this paper, we give a new theoretical error bound for this method for the case of diagonalizable matrices and also propose two improvements to speed up the convergence and reduce the effect of rounding errors. We also report the parallel performance of the method.