The algebraic eigenvalue problem
The algebraic eigenvalue problem
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Jacobi--Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils
SIAM Journal on Scientific Computing
ABLE: An Adaptive Block Lanczos Method for Non-Hermitian Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
An Inverse Free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems
SIAM Journal on Scientific Computing
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1
Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1
IRBL: An Implicitly Restarted Block-Lanczos Method for Large-Scale Hermitian Eigenproblems
SIAM Journal on Scientific Computing
An iterative block lanczos method for the solution of large sparse symmetric eigenproblems.
An iterative block lanczos method for the solution of large sparse symmetric eigenproblems.
Algorithm 845: EIGIFP: a MATLAB program for solving large symmetric generalized eigenvalue problems
ACM Transactions on Mathematical Software (TOMS)
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The inverse-free preconditioned Krylov subspace method of Golub and Ye [G.H. Golub, Q. Ye, An inverse free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems, SIAM J. Sci. Comp. 24 (2002) 312-334] is an efficient algorithm for computing a few extreme eigenvalues of the symmetric generalized eigenvalue problem. In this paper, we first present an analysis of the preconditioning strategy based on incomplete factorizations. We then extend the method by developing a block generalization for computing multiple or severely clustered eigenvalues and develop a robust black-box implementation. Numerical examples are given to illustrate the analysis and the efficiency of the block algorithm.