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Optimal quotients for solving large eigenvalue problems. (English) Zbl 1454.65023

This paper is devoted to find an optimal projection and resulting iterative methods to solve eigenvalue problems and generalized eigenvalue problems. At first, the notion of the optimal quotient is derived and basic properties of optimal quotients are proved. Then, several optimal quotient iterations are introduced and optimality conditions are shown. Finally, the idea of the optimal projection is extended to cover subspaces of a dimension larger than one. Significant numerical examples are discussed in details. Moreover, numerical experiments are presented which refer to an eigenvalue problem in magnetohydrodynamics (MHD) to illustrate convergence properties and computational cost of the presented algorithms.

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A22 Matrix pencils
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
76W05 Magnetohydrodynamics and electrohydrodynamics

Software:

JDQR; JDQZ
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Full Text: DOI Link

References:

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