Development of an Accurate Algorithm for exp(Bt).
CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS
Pagination or Media Count:
This document describes a program to compute the exponential of a given n by n matrix B multiplied by a scalar tau that is to be thought of as representing time. The authors primary goal has been to achieve as much accuracy as working precision permits without resorting to stimulated higher precision. The final product is more complicated than they anticipated at the outset. How these complications came to be expected is the theme of this story. The cases considered may be of interest to those who wish to use the matrix exponential in their work. The code acts simply on simple cases. This code is unlikely to be the last word on the computation of expBt since speed and simplicity deserve some recognition. For simplicity and generality this document considers only complex matrices and only those whose order n is small enough that four n by n arrays fit comfortably in the fast store. In practice the authors expect to have n100. Recall that unless B has special structure, such as being block diagonal, its exponential will have no zero elements. Additional keywords applies mathematics EISPACK computer program.
- Computer Programming and Software