On conjugate gradient-like methods for eigen-like problems |
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| Authors: | Alan Edelman Steven T. Smith |
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| Affiliation: | (1) Department of Mathematics, Massachusetts Institute of Technology, 02139 Cambridge, MA, USA;(2) Lincoln Laboratory, Massachusetts Institute of Technology, 02173 Lexington, MA, USA |
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| Abstract: | Numerical analysts, physicists, and signal processing engineers have proposed algorithms that might be called conjugate gradient for problems associated with the computation of eigenvalues. There are many variations, mostly one eigenvalue at a time though sometimes block algorithms are proposed. Is there a correct “conjugate gradient” algorithm for the eigenvalue problem? How are the algorithms related amongst themselves and with other related algorithms such as Lanczos, the Newton method, and the Rayleigh quotient? |
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| Keywords: | Conjugate gradient Lanczos Newton's Method optimization signal processing electronic structures differential geometry |
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