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A New Algorithm for the Symmetric Tridiagonal Eigenvalue Problem |
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| Institution: | Computer Science Department, State University of New York, Albany, New York 12222, and Mathematics and Computer Science Department, Lehman College, City University of New York, Bronx, New York 10468; Computer Science Department, Courant Institute, New York University, 251 Mercer Street, New York, New York and Computer Science Department, University of California, Berkeley, California 94720 |
| Abstract: | We apply a novel approach to approximate within ϵ to all the eigenvalues of an n × n symmetric tridiagonal matrix A using at most n2(3 log2(625n6)] + (83n − 34)log2 (log2((λ1 − λn)/(2ϵ))/log2(25n))]) arithmetic operations where λ1 and λn denote the extremal eigenvalues of A. The algorithm can be modified to compute any fixed numbers of the largest and the smallest eigenvalues of A and may also be applied to the band symmetric matrices without their reduction to the tridiagonal form. |
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