Preconditioned Eigensolvers: Practical Algorithms

Andrew V. Knyazev
June 15, 1999
URN = ncstrl.cudenver_ccm/UCD-CCM-143

Abstract: We propose a systematic review of preconditioned iterative methods for symmetric eigenvalue problems, separating the choice of the preconditioner and the choice of the iterative scheme. We describe several known methods, concentrating on algorithms and with just brief references to existing theory. We discuss, in some details, the algorithm of the recently suggested by the author Optimal Block Conjugate Gradient Method. We present numerical results showing that the method converges linearly with the optimal convergence rate. Numerical comparison establishes that our method is much faster than the Block Steepest Ascent Method when the same preconditioner is used in both methods. We discuss peculiarities of locking for preconditioned iterative eigensolvers.

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