A New Method Based on Continued Fraction for the Logarithms of Matrices

摘要

In the paper, we give the new method based on continued fraction for computing the logarithm of the matrix , it is called the matrix compressing and stretching method. It is different from the standard scaling and squaring method, it only need to times the matrix by 2~(-k). So the method can simplify and reduce the computation. When the diagonal elements are far greater than off-diagonal elements of matrix, the effect is obvious. It can be seen from the given numerical experiment. In the error analysis, the numerical accuracy of the methods are compared, the error bound theorem is given.