Isospectral flows and the inverse eigenvalue problem for Toeplitz matrices

✍ Scribed by Fasma Diele; Ivonne Sgura

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 248 KB
• Volume: 110
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(99)00193-4

✦ Synopsis

The inverse eigenvalue problem for Toeplitz matrices (ITEP), concerning the reconstruction of a symmetric Toeplitz matrix from prescribed spectral data, is considered. To numerically construct such a matrix the approach introduced by Chu in (SIAM Rev. 40(1) (1998) 1-39) is followed. He proposed to solve the ITEP by using an isospectral ow whose equilibria are symmetric Toeplitz matrices. In this paper we study the previous isospectral ow for reversed times and we obtain some formal properties of the solution. The case n = 3 for ITEP is analytically investigated by following an approach di erent from the one in (Chu, SIAM Rev. 40(1) (1998) 1-39). We prove that the ow globally converges to a regular Toeplitz matrix starting from a tridiagonal symmetric and centro-symmetric matrix. Numerical experiments conÿrm the above results and suggest their extension in higher dimension.