A fast method to block-diagonalize a Hankel matrix

作     者：Belhaj, Skander 

作者机构：Univ Franche Comte UFR Sci & Tech Math Lab CNRS UMR 6623 F-25030 Besancon France 

出 版 物：《NUMERICAL ALGORITHMS》 (数值算法)

年 卷 期：2008年第47卷第1期

页      面：15-34页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Hankel matrix block diagonalization triangular Toeplitz matrix Schur complementation 

摘      要：In this paper, we consider an approximate block diagonalization algorithm of an nxn real Hankel matrix in which the successive transformation matrices are upper triangular Toeplitz matrices, and propose a new fast approach to compute the factorization in O(n(2)) operations. This method consists on using the revised Bini method (Lin et al., Theor Comp Sci 315: 511-523, 2004). To motivate our approach, we also propose an approximate factorization variant of the customary fast method based on Schur complementation adapted to the nxn real Hankel matrix. All algorithms have been implemented in Matlab and numerical results are included to illustrate the effectiveness of our approach.