TY - JOUR

T1 - Computing the eigenvalues of symmetric H2-matrices by slicing the spectrum

AU - Benner, Peter

AU - Börm, Steffen

AU - Mach, Thomas

AU - Reimer, Knut

N1 - Funding Information:
The research of the third author was partially supported by the Research Council KU Leuven, fellowship F+/13/020 Exploiting Unconventional QR-Algorithms for Fast and Accurate Computations of Roots of Polynomials; and by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office, Belgian Network DYSCO (Dynamical Systems, Control, and Optimization). The research of the second and fourth authors was funded by the DFG Deutsche Forschungsgemeinschaft in project BO 3289/4-1.
Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.

PY - 2015/3/4

Y1 - 2015/3/4

N2 - 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 (Formula presented.) eigenvalues of the generalized symmetric eigenvalue problem in (Formula presented.) operations, where (Formula presented.) is a small constant.

AB - 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 (Formula presented.) eigenvalues of the generalized symmetric eigenvalue problem in (Formula presented.) operations, where (Formula presented.) is a small constant.

KW - $${\fancyscript{H}}^2$$H2-matrices

KW - Slicing the spectrum

KW - Symmetric generalized eigenproblem

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U2 - 10.1007/s00791-015-0238-y

DO - 10.1007/s00791-015-0238-y

M3 - Article

AN - SCOPUS:84923888517

VL - 16

SP - 271

EP - 282

JO - Computing and Visualization in Science

JF - Computing and Visualization in Science

SN - 1432-9360

IS - 6

ER -