Abstract
This paper presents a new Jacobi---Davidson type method to compute several real eigenvalues of the Hermitian quadratic eigenvalue problem. This method uses a simple index to sort the eigenvalues of the projected quadratic eigenvalue problem and extracts the approximate eigenvectors for the quadratic eigenvalue problem with the eigenvectors of the projected quadratic eigenvalue problem corresponding to the eigenvalues with the smallest indices. Numerical examples show that our method is effective and efficient to compute real eigenvalues of the Hermitian quadratic eigenvalue problem.
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