M. Wax, T. Kailath · IEEE Transactions on Acoustics Speech and Signal Processing · 1983
An iterative algorithm for the inversion of a Toeplitz-block Toeplitz matrix consisting of m × m blocks of size p × p is described. The algorithm presented exploits the structure of the Toeplitz-block Toeplitz matrix and outperforms Akaike's algorithm by a factor of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\max {2(p/m), 2}</tex> . The use of this algorithm for an iterative solution of a Toeplitz-block Toeplitz set of linear equations is also presented.
Cited by 111
S. Bensliman, M. Selmani, O. Khaldi · Computational Mathematics and Mathematical Physics · 2025
In this paper, we will study the product of a Toeplitz matrix with a kth-order slant Toeplitz matrix. We will find the necessary and sufficient conditions for this product to be a kth-order slant Toeplitz matrix.
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J. Pasupathy, R.A. Damodar · Linear Algebra and its Applications · 1992
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Begoña Cantó, Rafael Cantó, Ana M. Urbano · Axioms · 2025
In this work, combined matrices of tridiagonal Toeplitz matrices are studied. The combined matrix is known as the Relative Gain Array in control theory. In particular, given a real tridiagonal Toeplitz matrix of order n, the characterization of its combined matrix as a bisymmetric and doubly quasi-stochastic matrix is studied. Furthermore, this paper addresses the inverse problem, that is, given a bisymmetric, doubly quasi-stochastic tridiagonal Jacobi matrix U of order n, determine under what conditions there exists a real tridiagonal Toeplitz matrix A such that its combined matrix is U.
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Gover, M.J.C, Bradford Univ. (United Kingdom). School of Mathematical Sciences · OpenGrey (Institut de l'Information Scientifique et Technique) · 1988
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Ferrer Pascual, Maria · Dipòsit Digital de la Universitat de Barcelona (Universitat de Barcelona) · 2022
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: M. Eulàlia Montoro López
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D. Steven, Mackey Niloufer, Mackey Srdjan Petrovic · 1999
We show that every n × n complex nonderogatory matrix is similar to a unique unit upper Hessenberg Toeplitz matrix. The proof is constructive, and can be adapted to nonderogatory matrices with entries in any field of characteristic zero or characteristic greater than n. We also prove that every n × n complex matrix with n ≤ 4 is similar to a Toeplitz matrix. Key words. Toeplitz, Hessenberg, canonical form, inverse problem, nonderogatory.
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Georg Heinig, Karla Rost · Linear Algebra and its Applications · 1989
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M. Cristina Câmara, J. R. Partington · Journal of Operator Theory · 2017
Truncated Toeplitz operators and their asymmetric versions are studied in the context of the Hardy space $H^p$ of the half-plane for $1
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D. Steven Mackey, Niloufer Mackey, Srdjan Petrović · Linear Algebra and its Applications · 1999
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Corsetti, Matthew, Fokoué, Ernest · arXiv (Cornell University) · 2020
Nonnegative Matrix Factorization (NMF) is an unsupervised learning algorithm that produces a linear, parts-based approximation of a data matrix. NMF constructs a nonnegative low rank basis matrix and a nonnegative low rank matrix of weights which, when multiplied together, approximate the data matrix of interest using some cost function. The NMF algorithm can be modified to include auxiliary constraints which impose task-specific penalties or restrictions on the cost function of the matrix factorization. In this paper we propose a new NMF algorithm that makes use of non-data dependent auxiliary constraints which incorporate a Toeplitz matrix into the multiplicative updating of the basis and weight matrices. We compare the facial recognition performance of our new Toeplitz Nonnegative Matrix Factorization (TNMF) algorithm to the performance of the Zellner Nonnegative Matrix Factorization (ZNMF) algorithm which makes use of data-dependent auxiliary constraints. We also compare the facial recognition performance of the two aforementioned algorithms with the performance of several preexisting constrained NMF algorithms that have non-data-dependent penalties. The facial recognition performances are evaluated using the Cambridge ORL Database of Faces and the Yale Database of Faces.
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S. Twareque Ali, Miroslav Engliš · Hindustan Book Agency · 2007
Let Ω be a symplectic manifold, with symplectic form ω, and \( \mathcal{H} \) a subspace of L2(Ω, d µ), for some measure µ, admitting a reproducing kernel K. For φ ∈ C∞(Ω), the Toeplitz operator T φ with symbol φ is the operator on \( \mathcal{H} \) defined by $$ {{T}_{\phi }}f=P\left( {\phi f} \right),\:f\in \mathcal{H}, $$ where P: L2((Ω), d µ) → \( \mathcal{H} \) is the orthogonal projection. Using the reproducing kernel K, this can also be written as $${T_\phi }f(x) = \int_\Omega {d(y)\phi (y)K(x,y)d\mu (y)} .$$
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Israel Gohberg, Sonia Levin · Integral Equations and Operator Theory · 1978
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Georg Heinig · Contemporary mathematics - American Mathematical Society · 2001
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Bartosz Łanucha · Journal of Mathematical Analysis and Applications · 2013
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Shams Solary, Maryam · DSpace - Isik (Işık University) · 2024
In this paper we try to approximate any properties of quasi-block Toeplitz matrix (QBT), by means of a finite number of parameters. A quasi-block Toeplitz (QBT) matrix is a semi-infinite block matrix of the kind F = T(F) + E where T(F) = (Fj?k)j,k?Z, that Fk are m × m matrices such that ?i?Z|Fi| has bounded entries, and E = (ei,j )i,j?Z+ is a compact correction. Also, we should say the norms ? F ?w= ?i?Z ? Fi ? and ? E ?2 are finite. QBT-matrices are done with any given precision. The norm ? F ?QBT = ? ? F ?w + ? E ?2, is for ? = (1 + ?5)/2. These matrices are a Banach algebra with the standard arithmetic operations. We try to analysis some structures and computational properties for arithmetic operations of QBT matrices with some MATLAB commands.
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Aleksandra Kostić · Annals of DAAAM for ... & proceedings of the ... International DAAAM Symposium · 2011
In this note we bring a completely new strategy for calculating the minimum eigenvalue 1 (n) of a real symmetric, positive definite Toeplitz matrix (RSPDTM) T n . The strategy is particularly applicable to the modeling of secular functions, since it is based on a calculation of the smallest pole of secular functions. It is also pointed to structure of the array, which consists of the smallest eigenvalue of the main sub matrices of the RSPDTM T n
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Hamide Dogan, Luis R. Suarez · International Journal of Computing Algorithm · 2017
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William F. Trench, William F. Trench, William F. Trench · 1990
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Victor Y. Pan, John H. Reif · 1987
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