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Abstract : |
Abstract. In this paper we present an algorithm for the eigenvalue problem of symmetric tridiagonal matrices. Our algorithm employs the determinant evaluation, split-and-merge strategy and Laguerre's iteration. The method directly evaluates eigenvalues and uses inverse iteration as an option when eigenvectors are needed. This algorithm combines the advantages of existing algorithms such as QR, bisection/multisection and Cuppen's divide-and-conquer method. It is fully parallel, and competitive in speed with the most efficient QR algorithm in serial mode. On the other hand, our algorithm is as accurate as any standard algorithm for the symmetric tridiagonal eigenproblem and enjoys the flexibility in evaluating partial spectrum. Key words. eigenvalue, Laguerre's iteration, symmetric tridiagonal matrix, |
