Eigenvalue Problems on Infinite Intervals

Numerical Solution of singular Eigenvalue Problems for ODEs with a Focus on Problems Posed on Semi-Infinite Intervals

Boundary Value Problems for Functional Difference Equations on Infinite Intervals

INSTITUTE FOR ANALYSIS AND SCIENTIFIC COMPUTING VIENNA UNIVERSITY OF TECHNOLOGY Numerical Solution of Singular Eigenvalue Problems for ODEs with a Focus on Problems Posed on Semi-Infinite Intervals

This work is concerned with the computation of eigenvalues and eigenfunctions of singular eigenvalue problems (EVPs) arising in ordinary differential equations. Two different numerical methods to determine values for the eigenparameter such that the boundary value problem has nontrivial solutions are considered. The first approach incorporates a collocation method. In the course of this work th...

A rank-exploiting infinite Arnoldi algorithm for nonlinear eigenvalue problems

We consider the nonlinear eigenvalue problem: M(λ)x = 0, where M(λ) is a large parameter-dependent matrix. In several applications, M(λ) has a structure where the higher-order terms of its Taylor expansion have a particular low-rank structure. We propose a new Arnoldi based algorithm that can exploit this structure. More precisely, the proposed algorithm is equivalent to Arnoldi’s method applie...

Satisfiability Problems on Intervals and Unit Intervals

For an interval graph with some additional order constraints between pairs of non-intersecting intervals, we give a linear time algorithm to determine if there exists a realization which respects the order constraints. Previous algorithms for this problem (known also as seriation with side constraints) required quadratic time. This problem contains as subproblems interval graph and interval ord...