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A rational SHIRA method for the Hamiltonian eigenvalue problem. (English) Zbl 1207.65037
The paper deals with large, sparse generalized eigenvalue problems for matrix pencils, where one of the matrices is Hamiltonian and the other is skew-Hamiltonian. To this end the authors develop an algorithm which is a structure-preserving skew-Hamiltonian isotropic, implicitly restarted shift-and-invert Arnoldi algorithm. A numerical example is presented to confirm the efficiency of the new method – called “Rational SHIRA”.

MSC:
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A22 Matrix pencils
15B57 Hermitian, skew-Hermitian, and related matrices
65F50 Computational methods for sparse matrices
Software:
eigs
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