Preconditioned Eigensolvers	by Andrew Knyazev

What is "preconditioned eigensolvers?" In one sentence those are matrix-free iterative methods for partial eigenvalue problems that take advantage of using preconditioners to accelerate convergence. A complete answer can be found in the papers "Preconditioned eigensolvers - an oxymoron?" and Preconditioned eigensolvers by Andrew Knyazev. See also an article Andrew Knyazev, Volker Mehrmann, and Klaus Neymeyr, Preconditioning in Eigenvalue Computations, SIAM News, v. 35, no. 10, p. 9, December 2003. about Miniworkshop: Preconditioning in Eigenvalue Computations, 03.03. - 09.03.2002, Oberwolfach.

Preconditioned Eigensolvers related NSF grants

Preconditioned Eigensolvers People

General Software:

• Inverse Free Preconditioned Krylov Subspace Method (EIGIFP) by QIANG YE
• Jacobi-Davidson packages,
• Davidson program,
• Subspace Projected Approximate Matrix (SPAM) Modification of the Davidson Method,
• JDCG by Yvan Notay
• and my own favorite Locally Optimal Preconditioned Conjugate Gradient Method.

Specialized Software: Nonoverlap Domain Decomposition Preconditioning

Links:

• JD Gateway

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Parts of this material are based upon work supported by the National Science Foundation under Grants DMS 9501507, DMS 0208773, and DMS 0612751. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.