A new method based on continued fraction for the logarithms of matrices

作者：Li Chunjing; Zhang Linghong; Wang Minsi^*

来源：Journal of Information and Computational Science, 2010, 7(10): 2138-2142.

• Continued fraction
• Diagonal elements
• Error bound
• matrix
• Matrix compressing and stretching method
• Matrix logarithm
• Numerical accuracy
• Numerical experiments
• Off-diagonal elements
• Scaling and squaring method

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.

• 出版日期2010
• 单位同济大学