Global ETD Search

1	Fast and approximate computation of Laplace and Fourier transforms / Schnelle und approximative Berechnung von Laplace- und Fourier-Transformationen Melzer, Ines 04 April 2016 (has links) In this thesis, we treat the computation of transforms with asymptotically smooth and oscillatory kernels. We introduce the discrete Laplace transform in a modern form including a generalization to more general kernel functions. These more general kernels lead to specific function transforms. Moreover, we treat the butterfly fast Fourier transform. Based on a local error analysis, we develop a rigorous error analysis for the whole butterfly scheme. In the final part of the thesis, the Laplace and Fourier transform are combined to a fast Fourier transform for nonequispaced complex evaluation nodes. All theoretical results on accuracy and computational complexity are illustrated by numerical experiments. fast Laplace transform fast Fourier transform nonharmonic Fourier series real and complex exponential sums trigonometric approximation 65-02 - Research exposition ddc:510
2	The condition number of Vandermonde matrices and its application to the stability analysis of a subspace method / Die Konditionzahl von Vandermondematrizen und ihre Anwendung für die Stabilitätsanalyse einer Unterraummethode Nagel, Dominik 19 March 2021 (has links) This thesis consists of two main parts. First of all, the condition number of rectangular Vandermonde matrices with nodes on the complex unit circle is studied. The first time quantitative bounds for the extreme singular values are proven in the multivariate setting and when nodes of the Vandermonde matrix form clusters. In the second part, an optimized presentation of the deterministic stability analysis of the subspace method ESPRIT is given and results from the first part are applied. Vandermonde matrix stability analysis subspace method ESPRIT clustered nodes 31.40 - Analysis: Allgemeines 31.76 - Numerische Mathematik 31.80 - Angewandte Mathematik N40 - Numerical analysis I90 - Miscellaneous 65-02 - Research exposition G.1.0 - General G.1.3 - Numerical Linear Algebra ddc:510

Search results

Fast and approximate computation of Laplace and Fourier transforms / Schnelle und approximative Berechnung von Laplace- und Fourier-Transformationen

The condition number of Vandermonde matrices and its application to the stability analysis of a subspace method / Die Konditionzahl von Vandermondematrizen und ihre Anwendung für die Stabilitätsanalyse einer Unterraummethode