New inversion formulas for matrices classified in terms of their distance from Toeplitz 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...
متن کاملA note on inversion of Toeplitz matrices
It is shown that the invertibility of a Toeplitz matrix can be determined through the solvability of two standard equations. The inverse matrix can be denoted as a sum of products of circulant matrices and upper triangular Toeplitz matrices. The stability of the inversion formula for a Toeplitz matrix is also considered. c © 2007 Elsevier Ltd. All rights reserved.
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In this paper, motivated by Lin, Ching and Ng [Theoretical Computer Science, 315:511523 (2004)], a scaling version of Bini’s algorithm [SIAM J. Comput., 13:268-276 (1984)] for an approximate inversion of a triangular Toeplitz matrix is proposed. The scaling algorithm introduces a new scale parameter and is mathematically equivalent to the original Bini’s. Its computational cost is about two fas...
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j=1 yj φ(‖x − xj‖2), x ∈ R , where φ: [0,∞) → R is some given function, (yj) n 1 are real coefficients, and the centres (xj) n 1 are points in R. For a wide class of functions φ, it is known that the interpolation matrix A = (φ(‖xj − xk‖2)) n j,k=1 is invertible. Further, several recent papers have provided upper bounds on ‖A‖2, where the points (xj) n 1 satisfy the condition ‖xj − xk‖2 ≥ δ, j ...
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In this paper, we consider an inverse problem with the k-tridiagonal Toeplitz matrices. A theoretical result is obtained that under certain assumptions the explicit inverse of a ktridiagonal Toeplitz matrix can be derived immediately. Two numerical examples are given to demonstrate the validity of our results. (c) ٢٠١٢ Elsevier Ltd. All rights reserved.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1979
ISSN: 0024-3795
DOI: 10.1016/0024-3795(79)90030-2