Computing the minimum eigenvalue of symmetric positive definite Toeplitz matrix by Newton-type methods

摘要

A method for computing the smallest eigenvalue of a symmetric positive definite Toeplitz matrix by application of Newton's method to the characteristic polynomial has been recently introduced by Mastronardi and Boley [SIAM J. Sci. Comput., 20 (1999), pp. 1921-1927]. Though considerably slower than methods developed by the authors [W. Mackens and H. Voss, SIAM J. Matrix. Anal. Appl., 18 (1997), pp. 521-534], [W. Mackens and H. Voss, Linear Algebra Appl., 275/276 (1998), pp. 401-415], [H. Voss, Linear Algebra Appl., 287 (1999), pp. 359-371] the new approach is conceptually much simpler. In this paper we improve the performance of the new method substantially while keeping its simplicity. [References: 7]