Results 211 to 220 of about 26,208 (246)

A Proposal for Toeplitz Matrix Calculations

Studies in Applied Mathematics, 1986
In contrast to the usual (and successful) direct methods for Toeplitz systems Ax = b, we propose an algorithm based on the conjugate gradient method. The preconditioner is a circulant, so that all matrices have constant diagonals and all matrix‐vector multiplications use the Fast Fourier Transform. We also suggest a technique for the eigenvalue problem,
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The inverse of a symmetric banded toeplitz matrix

Reports on Mathematical Physics, 1997
A Toeplitz matrix is one whose \((i,j)\) entry depends only on the difference \(i-j\). The authors describe a method for obtaining an analytic form for the inverse of a finite symmetric banded Toeplitz matrix. For the tridiagonal case they rederive the explicit formula found by \textit{Hu} and \textit{O'Connell} [J. Phys. A: Math. Gen. 29, 1511 (1996)].
Lavis, D. A., Southern, B. W.
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On the Toeplitz and Polar Decompositions of an Involutive Matrix

Moscow University Computational Mathematics and Cybernetics, 2020
The Toeplitz decomposition of a square complex matrix \(A\) is its representation in the form \(A=B+iC, B=B^\ast , C=C^\ast.\) The Hermitian matrices \(B\) and \(C\) are determined uniquely by the formulas \(B={\frac{1}{2}}(A+A^\ast), C={\frac{1}{2i}}(A-A^\ast).\) The polar decompositions of \(A\) are its representations of the form \(A = PU = UQ ...
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The First Szegö Theorem for the Bergman–Toeplitz Matrix

Integral Equations and Operator Theory, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Yongning, Zhang, Ziliang, Zhao, Xianfeng, Zheng, Dechao   +3 more
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From matrix polynomial to determinant of block Toeplitz–Hessenberg matrix

Numerical Algorithms, 2023
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Toeplitz Jacobian Matrix for Nonlinear Periodic Vibration

Journal of Applied Mechanics, 1995
The main difference between a linear system and a nonlinear system is in the non-uniqueness of solutions manifested by the singular Jacobian matrix. It is important to be able to express the Jacobian accurately, completely, and efficiently in an algorithm to analyze a nonlinear system.
Leung, A. Y. T., Ge, T.
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The Inverse of a Finite Toeplitz Matrix

Technometrics, 1970
The inverse of this type of matrix is required in various areas of application of statistical, stochastic control and communication theory. Examples range over i) the fitting of autoregressive series (Siddiqui, 1958; Grenander and Rosenblatt, 1957), ii) the fitting of regression functions when the errors are serially correlated (Hannan, 1960; Whittle ...
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A symmetric rank-revealing toeplitz matrix decomposition

Journal of VLSI signal processing systems for signal, image and video technology, 1996
Summary: In signal and image processing, regularization often requires a rank-revealing decomposition of a symmetric Toeplitz matrix with a small rank deficiency. In this paper, we present an efficient factorization method that exploits symmetry as well as the rank and Toeplitz properties of the given matrix.
Luk, Franklin T., Qiao, Sanzheng
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Approximation by a Hermitian Positive Semidefinite Toeplitz Matrix

SIAM Journal on Matrix Analysis and Applications, 1993
The authors study the problem of finding the closest Hermitian positive semidefinite Toeplitz matrix of a given rank to an arbitrary given matrix (in the Frobenius norm = Hilbert-Schmidt norm). They introduce two methods, one is based on using a special orthonormal basis in the space of Hermitian Toeplitz matrices and the second is a modified ...
Suffridge, T. J., Hayden, T. L.
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Least squares Toeplitz matrix solutions of the matrix equation

Linear and Multilinear Algebra, 2016
AbstractLet and we first solve the minimum Frobenius norm residual problem (Problem LSP): with unknown Toeplitz matrices X and Y. We then consider a best approximation problem: given Toeplitz matrices and , find such that where is the solution set of Problem LSP.
Yongxin Yuan, Wenhua Zhao, Hao Liu
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