A new algebra of Toeplitz-plus-Hankel matrices and applications
نویسندگان
چکیده
منابع مشابه
Generalized inversion of Toeplitz-plus-Hankel matrices
In many applications, e.g. digital signal processing, discrete inverse scattering, linear prediction etc., Toeplitz-plus-Hankel (T + H) matrices need to be inverted. (For further applications see [1] and references therein). Firstly the T +H matrix inversion problem has been solved in [2] where it was reduced to the inversion problem of the block Toeplitz matrix (the so-called mosaic matrix). T...
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When the heat equation and wave equation are approximated by ut = −Ku and utt = −Ku (discrete in space), the solution operators involve e−Kt, √K, cos(√Kt), and sinc( √ Kt). We compute these four matrices and find accurate approximations with a variety of boundary conditions. The second difference matrix K is Toeplitz (shift-invariant) for Dirichlet boundary conditions, but we show why e−Kt also...
متن کاملKronecker product approximations for dense block Toeplitz-plus-Hankel matrices
In this paper, we consider the approximation of dense block Toeplitz-plus-Hankel matrices by sums of Kronecker products. We present an algorithm for efficiently computing the matrix approximation that requires the factorization of matrices of much smaller dimension than that of the original. The main results are described for block Toeplitz matrices with Toeplitz-plus-Hankel blocks (BTTHB), but...
متن کاملIrreducible Toeplitz and Hankel matrices
An infinite matrix is called irreducible if its directed graph is strongly connected. It is proved that an infinite Toeplitz matrix is irreducible if and only if almost every finite leading submatrix is irreducible. An infinite Hankel matrix may be irreducible even if all its finite leading submatrices are reducible. Irreducibility results are also obtained in the finite cases.
متن کاملSplit Algorithms and ZW-Factorization for Toeplitz and Toeplitz-plus-Hankel Matrices
New algorithms for Toeplitz and Toeplitz-plus-Hankel are presented that are in the spirit of the “split” algorithms of Delsarte/Genin. It is shown that the split algorithms are related to ZW-factorizations like the classical algorithms are related to LU-factorizations. Special attention is paid to skewsymmetric Toeplitz, centrosymmetric Toeplitz-plus-Hankel and general Toeplitz-plus-Hankel matr...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2008
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2007.09.006