Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals.
Explicit formulas for the constituent matrices. Application to the matrix functions
We present a constructive procedure for establishing explicit formulas of the constituents matrices. Our approach is based on the tools and techniques from the theory of generalized Fibonacci sequences. Some connections with other results are supplied. Furthermore,we manage to provide tractable expressions for the matrix functions, and for illustration purposes we establish compact formulas for both the matrix logarithm and the matrix pth root. Some examples are also provided.