Numerical simulation of three dimensional pyramid quantum dot
Journal of Computational Physics
Reducing sparse nonlinear eigenproblems by automated multi-level substructuring
Advances in Engineering Software
Critical delays and polynomial eigenvalue problems
Journal of Computational and Applied Mathematics
Saving flops in LU based shift-and-invert strategy
Journal of Computational and Applied Mathematics
A Krylov Method for the Delay Eigenvalue Problem
SIAM Journal on Scientific Computing
Rational krylov for large nonlinear eigenproblems
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
An overview on the eigenvalue computation for matrices
Neural, Parallel & Scientific Computations
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The rational Krylov algorithm computes eigenvalues and eigenvectors of a regular not necessarily symmetric matrix pencil. It is a generalization of the shifted and inverted Arnoldi algorithm, where several factorizations with different shifts are used in one run. It computes an orthogonal basis and a small Hessenberg pencil. The eigensolution of the Hessenberg pencil approximates the solution of the original pencil. Different types of Ritz values and harmonic Ritz values are described and compared. Periodical purging of uninteresting directions reduces the size of the basis and makes it possible to compute many linearly independent eigenvectors and principal vectors of pencils with multiple eigenvalues. Relations to iterative methods are established.Results are reported for two large test examples. One is a symmetric pencil coming from a finite element approximation of a membrane; the other is a nonsymmetric matrix modeling an idealized aircraft stability problem.