author: Mackens, W.; Voss, H.
shorttitle: Computing the minimum eigenvalue ....
source: SIAM J. Sci. Comput. 21, No. 4, 1650 - 1656 (2000)
keywords:Toeplitxz matrix .. eigenvalue .. Newton's method
revtext: For the positive definite Toeplitz matrix the smallest eigenvalue (i.e., root of the secular polynomial) is sought. Reference is made to the author's own work (viz., projection method, extrapolating in effect the separate iterates and being the quickest one on the market) and to the method by Mastronardi and Boley (using the Newton's root search). The conceptual simplicity of the latter approach is then combined with the former encouraging experience with the preservation and maximal fructification of all the information amassed during the iteration process. The new algorithm is proposed and shown to combine these merits. Empirically, the Hermitian interpolations proved to beat the Lagrangian ones, and the Newton steps proved better than the mere secant ones.