An Improved Taylor Algorithm for Computing the Matrix Logarithm

The most popular method for computing the matrix logarithm is a combination of inverse scaling and squaring in conjunction with Padé approximation, sometimes accompanied by Schur decomposition. In this work, we present Taylor series algorithm, based on free-transformation approach technique, that uses recent polynomial formulas evaluating approximation more efficiently than Paterson–Stockmeyer method. Two MATLAB implementations related to relative forward or backward error analysis, were developed compared different state-of-the art functions. Numerical tests showed new are generally accurate previously available codes, an intermediate execution time among all codes comparison.