Toeplitz-plus-Hankel Bezoutians and inverses of Toeplitz and Toeplitz-plus-Hankel matrices
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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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.
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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...
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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...
متن کاملTransformation Techniques for Toeplitz and Toeplitz-plus-Hankel Matrices. I. Transformations
Transformations of the form A + E’FAg2 are investigated that transform Toeplitz and Toeplitz-plus-Hankel matrices into generalized Cauchy matrices. ‘Zi and @a are matrices related to the discrete Fourier transformation or to various real trigonometric transformations. Combining these results with pivoting techniques, in paper II algorithms for Toeplitz and Toeplitz-plus-Hankel systems will be p...
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ژورنال
عنوان ژورنال: Operators and Matrices
سال: 2008
ISSN: 1846-3886
DOI: 10.7153/oam-02-23