Computing the eigenvalues of symmetric H2-matrices by slicing the spectrum

The computation of eigenvalues of large-scale matrices arising from finite element discretizations has gained significant interest in the last decade (Knyazev et al. in Numerical solution of PDE eigenvalue problems, vol 56. Mathematisches Forschungsinstitut, Oberwolfach, 2013 ). Here we present an n...

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Bibliographic Details
Published inComputing and visualization in science Vol. 16; no. 6; pp. 271 - 282
Main Authors Benner, Peter, Börm, Steffen, Mach, Thomas, Reimer, Knut
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2013
Subjects
Algorithms
Calculus of Variations and Optimal Control; Optimization
Computational Mathematics and Numerical Analysis
Computer Applications in Chemistry
Mathematics
Mathematics and Statistics
Numerical Analysis
Visualization
65F50
65F15
matrices
Symmetric generalized eigenproblem
Slicing the spectrum
15A18
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Summary:The computation of eigenvalues of large-scale matrices arising from finite element discretizations has gained significant interest in the last decade (Knyazev et al. in Numerical solution of PDE eigenvalue problems, vol 56. Mathematisches Forschungsinstitut, Oberwolfach, 2013 ). Here we present an new algorithm based on slicing the spectrum that takes advantage of the rank structure of resolvent matrices in order to compute m eigenvalues of the generalized symmetric eigenvalue problem in O ( n m log α n ) operations, where α > 0 is a small constant.
ISSN:1432-9360
1433-0369
DOI:10.1007/s00791-015-0238-y