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A Proposal for Toeplitz Matrix Calculations
Studies in Applied Mathematics, 1986In 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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Parallel algorithms for Toeplitz matrix operations
ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005Algorithms for multiplication and inversion of ToepIitz matrices are presented that take advantage of the special structure of ToepIitz forms and the parallelism offered by concurrent processors. Multiplication of two general n×n Toeplitz matrices is defined on an array of 2n-1 processing elements.
C. Price, M. Salama
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Approximate Toeplitz Matrix Problem Using Semidefinite Programming
Journal of Optimization Theory and Applications, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Least squares Toeplitz matrix solutions of the matrix equation
Linear and Multilinear Algebra, 2016AbstractLet 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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Hyponormal Toeplitz Operators with Matrix-Valued Circulant Symbols
Complex Analysis and Operator Theory, 2011Let \(L^2 = L^2(\mathbb{T})\) be the set of all square-integrable functions on the unit circle \(\mathbb{T} = \partial \mathbb{D}\) in the complex plane, \(H^2 = H^2(\mathbb{T})\) be the corresponding Hardy space and \(H^\infty = L^\infty \cap H^2\). Let \(M_n\) denote the set of \(n \times n\) complex matrices. Then \( L^2_{\mathbb{C}^n} = L^2 \otimes
Hwang, In Sung +2 more
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Approximation by a Hermitian Positive Semidefinite Toeplitz Matrix
SIAM Journal on Matrix Analysis and Applications, 1993The 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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SQP algorithms for solving Toeplitz matrix approximation problem
Numerical Linear Algebra with Applications, 2002AbstractGiven an n × n matrix F, we find the nearest symmetric positive semi‐definite Toeplitz matrix T to F. The problem is formulated as a non‐linear minimization problem with positive semi‐definite Toeplitz matrix as constraints. Then a computational framework is given.
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The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
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