Accuracy Improvement of Newton's Method for the Matrix Logarithm

Abstract

Abstract. Logarithms of matrices defined as inverse function of exponentials of matrices arise in control theory and others. One of the algorithm that evaluate the logarithm called inverse scaling and squaring is constructed with matrix square root and Padé approximants, In this algorithm, product form DB iteration that is a variation of Newton’s method is applied to matrix square root. However, the algorithm may cause significant digit loss. So in this article, we propose a new iteration based on product form DB iteration to avoid the significant digit loss, and show the results of numerical experiments to compare their iterations.