Austrian Academy of Sciences
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Bruck an der Leitha
Stadt im östlichen Niederösterreich an der Grenze zum Burgenland, bis 1918 Grenzstadt zur ungarischen Reichshälfte der Habsburger-Doppelmonarchie
Abgekürzt zitierte Literatur - Verzeichnis der im Text und Katalog verwendeten Abkürzungen - Abbildungsnachweis. Forschungen in Limyra|Studien zum kaiserzeitlichen Tafelgeschirr aus Limyra|
XII. KONKORDANZ DER FUNDE MIT DEN HAUSKONTEXTEN UND DEN STRATIGRAPHISCHEN EINHEITEN. Veröffentlichung der Mykenischen Kommission|Aigeira 2. Die Mykenische Akropolis. Grabungen 1975-1980|
Hypergraph edge elimination - A symbolic phase for Hermitian eigensolvers based on rank-1 modifications. ETNA - Electronic Transactions on Numerical Analysis
It is customary to identify sparse matrices with the corresponding adjacency or incidence graphs. For the solution of a linear system of equations using Gaussian elimination, the representation by its adjacency graph allows a symbolic factorization that can be used to predict memory footprints and enables the determination of near-optimal elimination orderings based on heuristics. The Hermitian eigenvalue problem on the other hand seems to evade such treatment at first glance due to its inherent iterative nature. In this paper we prove this assertion wrong by revealing a tight connection of Hermitian eigensolvers based on rank-1 modifications with a symbolic edge elimination procedure. A symbolic calculation based on the incidence graph of the matrix can be used in analogy to the symbolic phase of Gaussian elimination to develop heuristics which reduce memory footprint and computations. Yet, we also show that the question of an optimal elimination strategy remains NP-complete, in analogy to the linear systems case