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Abstract: The differential equation = [X; k(X)] where k is a Toeplitz annihilator has been suggested as a means to solve the inverse Toeplitz eigenvalue problem. Starting with the diagonal matrix whose entries are the same as the given eigenvalues, the solution flow has been observed numerically to always converge a symmetric Toeplitz matrix as t \Gamma! 1. This paper is an attempt to understand the dynamics involved in the case n = 3. (Update)
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BibTeX entry: (Update)
@misc{ toeplitz-differential,
author = "Where Is Toeplitz",
title = "On the Differential Equation",
url = "citeseer.ist.psu.edu/759914.html" }
Citations (may not include all citations):235 Classical Mechanics (context) - Goldstein - 1965
142 Advanced Mathematical Methods for Scientists and Engineers (context) - Bender, Orszag - 1978
122 Theory of Ordinary Differential Equations (context) - Coddington, Levinson - 1955
44 Computer Solution of Ordinary Differential Equations: The In.. (context) - Shampine, Gordon - 1975
31 The formulation and analysis of numerical methods for invers.. (context) - Friedland, Nocedal et al. - 1987
22 Matrix Theory (context) - Gantmacher - 1959
18 The theory of Grobner bases (context) - Pauer, Pfeifhofer - 1988
13 Qualitative Theory of Ordinary Differential Equations (context) - Brauer, Nohel - 1969
11 Spectral properties of finite Toeplitz matrices (context) - Delsarte, Genin - 1983
8 A numerical approach to the inverse Toeplitz eigenproblem SI.. (context) - Laurie - 1988
8 Can real symmetric Toeplitz matrices have arbitrary real spe.. (context) - Driessel, Chu
6 Matrix differential equations: A continuous realization proc.. (context) - Chu - 1990
4 Continuous and Discrete Dynamics near Manifolds of Equilibri.. (context) - Aulbach - 1980
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