On inverse eigenvalue problems for block Toeplitz matrices with Toeplitz blocks

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• 作者：Zhongyun Liu ; Yulin Zhang ; C. Ferreira ; Rui Ralha
• 关键词：Block Toeplitz matrix ; Generalized K-centrosymmetric matrix ; Inverse eigenvalue problem ; Newton method
• 刊名：Applied Mathematics and Computation
• 出版年：2010
• 出版时间：15 May 2010
• 年：2010
• 卷：216
• 期：6
• 页码：1819-1830
• 全文大小：611 K

文摘

We propose an algorithm for solving the inverse eigenvalue problem for real symmetric block Toeplitz matrices with symmetric Toeplitz blocks. It is based upon an algorithm which has been used before by others to solve the inverse eigenvalue problem for general real symmetric matrices and also for Toeplitz matrices. First we expose the structure of the eigenvectors of the so-called generalized centrosymmetric matrices. Then we explore the properties of the eigenvectors to derive an efficient algorithm that is able to deliver a matrix with the required structure and spectrum. We have implemented our ideas in a Matlab code. Numerical results produced with this code are included.