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Homogeneous Jacobi-Davidson. (English) Zbl 1171.65377

Summary: We study a homogeneous variant of the Jacobi-Davidson method for the generalized and polynomial eigenvalue problem. While a homogeneous form of these problems was previously considered for the subspace extraction phase, in this paper this form is also exploited for the subspace expansion phase and the projection present in the correction equation. The resulting method can deal with both finite and infinite eigenvalues in a natural and unified way. We show relations with the multihomogeneous Newton method, Rayleigh quotient iteration, and (standard) Jacobi-Davidson for polynomial eigenproblems.

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F50 Computational methods for sparse matrices
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