Numerical Solution of the Inverse Eigenvalue Problem for Real Symmetric Toeplitz Matrices

Authors:
William F. Trench
Affiliations:
-
Venue:
SIAM Journal on Scientific Computing
Year:
1997

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Abstract

H. J. Landau has recently given a nonconstructive proof of an existence theorem for the inverse eigenvalue problem for real symmetric Toeplitz (RST) matrices. This paper presents a procedure for the numerical solution of this problem. The procedure is based on an implementation of Newton's method that exploits Landau's theorem and other special spectral properties of RST matrices. With this version of Newton's method, together with the strategy proposed for applying it, the method appears to be globally convergent; however, this is not proved.