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The Jacobi-Davidson method, proposed by Gerard Sleijpen and Henk van der Vorst in 1996, is often a competitive eigensolver, in particular when interior eigenvalues are sought, a preconditioner for the matrix is available, or generalized eigenproblems are considered. Follow the links to find out more, and please email me at m.e.hochstenbach tue.nl with suggestions for additions and improvements.
Michiel Hochstenbach
TU Eindhoven