Journal ArticleDOI
On an iterative method for finding lovver eigenvalues
E. G. D’Yakonov,Andrew Knyazev +1 more
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TLDR
The analysis of the errors involved in approximate orthogonalization with respect to previously found eigenvectors in preconditioned iterations of a subspace for simultaneous determination of a cluster of eigenvalues and the corresponding eigenvctors of a large sparse symmetrical eigenvalue problem is presented.Abstract:
We present the analysis of the errors involved in approximate orthogonalization with respect to previously found eigenvectors in preconditioned iterations of a subspace for simultaneous determination of a cluster of eigenvalues and the corresponding eigenvectors of a large sparse symmetrical eigenvalue problem.read more
Citations
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Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
TL;DR: Numerical results establish that the LOBPCG method is practically as efficient as the ``ideal'' algorithm when the same preconditioner is used in both methods, and direct numerical comparisons with the Jacobi--Davidson method show that the method is more robust and converges almost two times faster.
Journal ArticleDOI
Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in hypre and PETSc
TL;DR: Numerically the scalability of BLOPEX is demonstrated by testing it on a number of distributed and shared memory parallel systems, including a Beowulf system, SUN Fire 880, an AMD dual-core Opteron workstation, and IBM BlueGene/L supercomputer, using PETSc domain decomposition and hypre multigrid preconditioning.
Journal ArticleDOI
A Subspace Preconditioning Algorithm For Eigenvector/Eigenvalue Computation
TL;DR: An effective parallelizable technique for computing eigenvalues and eigenvectors utilizing subspace iteration and preconditioning for a symmetric positive definite operatorA defined on a finite dimensional real Hilbert spaceV is developed.
Efficient solution of symmetric eigenvalue problems using multigridpreconditioners in the locally optimal block conjugate gradient method
A. Knyazev,K. Neymeyr +1 more
TL;DR: Results of numerical tests are presented, which demonstrate practical effectiveness of the approach for the locally optimal block conjugate gradient method preconditioned by the standard V-cycle multigrid applied to the stiffness matrix.
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A posteriori error estimation for elliptic eigenproblems
TL;DR: An a posteriori error estimator is presented for a subspace implementation of preconditionsed inverse iteration, which derives from the well‐known inverse iteration in such a way that the associated system of linear equations is solved approximately by using a preconditioner.
References
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Journal ArticleDOI
Convergence rate estimates for iterative methods for a mesh symmetrie eigenvalue problem
TL;DR: In this article, the authors considered a symmetric partial algebraic eigenvalue problem and analyzed the convergence rates of several methods of solving it by means of a preconditioner.