Chebyshev-Hankel matrices and the splitting approach for centrosymmetric Toeplitz-plus-Hankel matrices

摘要

Centrosymmetric Toeplitz-plus-Hankel matrices are investigated on the basis of their "splitting property", which is their similarity to the direct sum of two special Toeplitz-plus-Hankel matrices. These matrices can be considered as Hankel matrices (moment matrices) in bases of Chebyshev polynomials and are called Chebyshev-Hankel matrices. Chebyshev-Hankel matrices have similar properties like Hankel matrices. This concerns inversion formulas and fast algorithms. A superfast algorithm for solving Chebyshev-Hankel and centrosymmetric Toeplitz-plus-Hankel systems is presented that is based on real trigonometric transforms. The main tool of investigation is the interpretation of Chebyshev-Hankel matrices as matrices of restricted multiplication operators with respect to Chebyshev bases. (C) 2001 Elsevier Science Inc. All rights reserved. [References: 21]