Scaling and modified squaring method for the matrix exponential

抄録

In recent years, many discrete variable methods using the exponential operator, called exponential integrator, have been presented, and various computational methods of the matrix exponential are also proposed. Especially the combination of the Padé approximant and the scaling and squaring method is most powerful and widely used. However, the squaring process is susceptible to roundoff errors. We propose a modified squaring process for the scaling and squaring methods. From the numerical results, an accuracy improvement about 1/100 is obtained in the best case.