24 October, 2010

Eigen Solvers

Eigen Solver:


Current Eigensolvers

Unlike ARPACK, which provides a single eigensolver, Anasazi provides a framework capable of describing a wide variety of eigenproblems and algorithms for solving them. Anasazi can currently solve complex and real, Hermitian and non-Hermitian, eigenvalue problems, via the following included methods:

* Block Krylov-Schur method, a block extension of A Krylov-Schur Algorithm for Large Eigenproblems, G. W. Stewart, SIAM J. Matrix Anal. Appl., 23, pp. 601-614 (2000).
* Block Davidson method described in A Comparison of Eigensolvers for Large-scale 3D Modal Analysis Using AMG-Preconditioned Iterative Methods, P. Arbenz, U. L. Hetmaniuk, R. B. Lehoucq, R. S. Tuminaro, Internat. J. for Numer. Methods Engrg., 64, pp. 204-236 (2005)
* LOBPCG, a stable implementation of Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method, SIAM J. Sci. Comput., 23 (2001), pp. 517-541, as described in Basis selection in LOBPCG, U. L. Hetmaniuk and R. B. Lehoucq, J. Comput. Physics, 218, pp. 324-332 (2006)
* IRTR, an implicit version of the Riemannian Trust-Region Eigensolver, orginally described in A truncated-CG style method for symmetric generalized eigenvalue problems, P.-A. Absil, C. G. Baker, and K. A. Gallivan, J. Computational and Applied Mathematics, 189, pp. 274-285 (2006).

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