Efficient computation of the action of matrix rational functions and Laplace transforms / eingereicht von Manuel Tsolakis, M.Sc. Wuppertal, 28. April 2023
Content
Introduction
Review of basic material
Relevant classes of functions
Continued fractions
Definition of matrix functions
Krylov subspace methods for general matrix functions
The Arnoldi approximation
The restarted Arnoldi method
Error bounds for the restarted Arnoldi method
Iterative methods for rational matrix functions
Matrix pencils
CF-matrices
Restarts for Laplace transforms
A new representation of the error function
Implementational aspects
Quadrature
Breaking the recursion
Matrix exponential function
Modifications for complete Bernstein functions
Numerical experiments I: Comparison to other methods
Fractional negative power less than -1
Fractional diffusion processes on graphs
Gamma function
Square root
Entropy
Error bounds
A priori bound I: Finite integration interval
A priori bound II: Exponentially bounded integrand
A priori bound III: Main case
A posteriori bound
Numerical experiments II: Error bounds
Conclusions
Other definitions of the Laplace transform
Bibliography