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