A fully parallel method for the singular eigenvalue problem |
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Affiliation: | Department of Mathematics and Statistics University of West Florida, Pensacola, FL 32514, U.S.A.;Department of Mathematics Beijing Jiaotong University Beijing, P.R. China |
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Abstract: | In this paper, a fully parallel method for finding some or all finite eigenvalues of a real symmetric matrix pencil (A, B) is presented, where A is a symmetric tridiagonal matrix and B is a diagonal matrix with b1 > 0 and bi ≥ 0, i = 2,3,…,n. The method is based on the homotopy continuation with rank 2 perturbation. It is shown that there are exactly m disjoint, smooth homotopy paths connecting the trivial eigenvalues to the desired eigenvalues, where m is the number of finite eigenvalues of (A, B). It is also shown that the homotopy curves are monotonic and easy to follow. |
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