Matrix functions approximation for square matrices using Newton’s interpolation

Abstract

In this paper, we propose different formulas to approximating matrix functions for square matrices having (mixed or pure complex) eigenvalues. The suggested formulas are deduced from Newton’s divided differences which defined for square matrices having real eigenvalues where we generalize it in our proposal cases. The theoretical analysis of these techniques is then discussed. Numerical examples are presented to illustrate the applicability and the accuracy of the obtained analytical results.