The matrix logarithm is frequently used in control theory, machine learning, and other fields. Inverse scaling and squaring is a well-known method to approximate matrix logarithms. This method is based on Newton’s iteration and Padé approximants. Therefore, the truncation error of Newton’s iteration affects the approximation accuracy of the method. The stopping criterion for Newton’s iteration to bound the absolute error by the specified value is proposed. We introduce adjusted degree of the truncated Taylor series to the algorithm in order to make the relative error bounded.

matrix logarithm, inverse scaling and squaring, specified relative accuracy.