Eigenvalue algorithm

Known as: Eigensolver, Matrix eigenvalue problem, Symbolic computation of matrix eigenvalues 
In numerical analysis, one of the most important problems is designing efficient and stable algorithms for finding the eigenvalues of a matrix, or… (More)
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41 relations
AlgorithmArnoldi iterationBisection methodCentrality
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Numerical linear algebra

Papers overview

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2012
2012
A linear eigenvalue algorithm for the nonlinear eigenvalue problem
The Arnoldi method for standard eigenvalue problems possesses several attractive properties making it robust, reliable and… (More)
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Highly Cited
2011
Highly Cited
2011
Parallel solution of partial symmetric eigenvalue problems from electronic structure calculations
The computation of selected eigenvalues and eigenvectors of a symmetric (Hermitian) matrix is an important subtask in many… (More)
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2010
2010
A Fast Implicit QR Eigenvalue Algorithm for Companion Matrices
An implicit version of the shifted QR eigenvalue algorithm given in [D. A. Bini, Y. Eidelman, I. Gohberg, L. Gemignani, SIAM J… (More)
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2010
2010
On perturbations of quasiperiodic Schrödinger operators
Using relative oscillation theory and the reducibility result of Eliasson, we study perturbations of quasiperiodic Schrödinger… (More)
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2008
2008
Eigenvalue asymptotics for randomly perturbed non-selfadjoint operators
  • Mildred Hager, Johannes Sjoestrand
  • 2008
We consider quite general h-pseudodifferential operators on R with small random perturbations and show that in the limit h → 0… (More)
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2007
2007
Fast QR Eigenvalue Algorithms for Hessenberg Matrices Which Are Rank-One Perturbations of Unitary Matrices
Let Hn ⊂ Cn×n be the class of n × n Hessenberg matrices A which are rank-one modifications of a unitary matrix, that is, A = H… (More)
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2001
2001
Large-scale eigenvalue calculations for stability analysis of steady flows on massively parallel computers
  • Richard B. Lehoucq, Andrew G. Salinger
  • 2001
We present an approach for determining the linear stability of steady states of PDEs on massively parallel computers. Linearizing… (More)
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1999
1999
A PARALLEL DIVIDE AND CONQUER ALGORITHM FOR THE SYMMETRIC EIGENVALUE PROBLEM ON DISTRIBUTED MEMORY ARCHITECTURES
  • S SIAMJ.
  • 1999
We present a new parallel implementation of a divide and conquer algorithm for computing the spectral decomposition of a… (More)
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1997
1997
The BR Eigenvalue Algorithm
T h e B R algorithm, a new method for calculating the eigenvalues of an upper Hessenberg matrix, is introduced. I t is a bulge… (More)
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Highly Cited
1988
Highly Cited
1988
Mode localization and eigenvalue loci veering phenomena in disordered structures
An investigation of the effects of disorder on the modes of vibration of nearly periodic structures is presented. It is shown… (More)
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