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Bounds for the decay in matrix functions and its exploitation in matrix computations / eingereicht von Claudia Schimmel, M. Ed. Wuppertal, 01.10.2019
Inhalt
Abstract
Contents
Introduction
Review of basic material
Functions of matrices
Basic definitions
Computational aspects
Graph theory
Minimal polynomials
Chebyshev polynomials
Faber polynomials
Bounds for the decay in functions of matrices
Relation between decay in matrix functions and polynomial approximation
Bounds for the inverse
Literature review
New results
Comparison and numerical examples
Bounds with non-Toeplitz structure
Bounds for functions defined by an integral transform
Literature review
New results
Comparison and numerical examples
Exploiting the decay in matrix functions
Preliminaries: The computation of a distance-d coloring
Sparse approximations of functions of matrices
Computing a sparse approximation
Numerical examples
Approximation of f(A)v
Exploiting the decay for the computation of f(A)v
Numerical examples
Approximation of the trace of matrix functions
Acceleration of the basic Monte Carlo method
Non-stochastic approximation
Conclusions
Acknowledgements
List of Figures
List of Tables
List of Algorithms
List of Notations
Bibliography