Variations on Harmonic Rayleigh–ritz for Standard and Generalized Eigenproblems
نویسنده
چکیده
We present several variations on the harmonic Rayleigh–Ritz method. First, we introduce a relative harmonic approach for the standard, generalized, and polynomial eigenproblem. Second, a harmonic extraction method is studied for rightmost eigenvalues of generalized eigenvalue problems. Third, we propose harmonic extraction methods for large eigenvalues of generalized and polynomial eigenproblems, where we also discuss avoidance of infinite eigenvalues when the finite eigenvalues are of interest. We give an oversight of the different methods with their relations and several typical numerical examples. AMS subject classifications. 65F15, 65F50.
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