Results 181 to 190 of about 480 (210)

O(nlog2n) determinant computation of a Toeplitz matrix and fast variance estimation [PDF]

Applied Mathematics Letters, 1996
The determinant of an n × n Toeplitz matrix can be computed in O(n) flops given the associated generalised Shur constants, and these can be found from the fast algorithms of de Hoog and Ammar and Gragg without increasing the algorithms' asymptotic ...
Dietrich, C.R., Osborne, M.R.
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The determinants of certain (0,1) Toeplitz matrices

Linear Algebra and its Applications, 2021
This paper deals with pentadiagonal Toeplitz matrices, namely square Toeplitz matrices with four subdiagonals, two above and two below the main diagonal, that are nonzero (see [\textit{M. Andelić} and \textit{C. M. da Fonseca}, ``Some determinantal considerations for pentadiagonal matrices'', Linear Multilinear Algebra (to appear), \url{doi:10.1080 ...
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An explicit formula for the determinants of tridiagonal $2$-Toeplitz and $3$-Toeplitz matrices

Annals of Mathematical Sciences and Applications, 2023
A tridiagonal matrix is a \(k\)-Toeplitz matrix if its diagonals are \(k\)-periodic. The author gives an explicit formula for its determinant when \(k=2\) or \(k=3\).
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Toeplitz determinants and positive semidefiniteness

IEEE Transactions on Signal Processing, 1991
The role that the determinants of real, symmetric, Toeplitz matrices play in testing for their positive semidefiniteness is discussed. It is shown that the leading principal minor test is not sufficient in general to test for the positive semidifiniteness of Toepliz matrices, except in certain cases.
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On Asymptotics of Toeplitz Determinants with Symbols of Nonstandard Smoothness

Journal of Fourier Analysis and Applications, 2004
Let \(\mathbb T\) denote the unit circle. For a function \(a\in L^1(\mathbb T)\) and an integer \(n\geq 0\), the \(n\)-th Toeplitz determinant \(D_n(a)\) is given by \(D_n(a)=\det(a_{j-k})_{j,k=0}^n\) where \(a_i\) is the \(i\)-th Fourier coefficient of \(a\). In 1952, G. Szegő proved that if \(a\in C^{1+\epsilon}\) and \(a\geq 0\), then \[ \lim_{n\to \
Karlovich, Alexei Yu., Santos, Pedro A.
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On a relationship between Chebyshev polynomials and Toeplitz determinants

Applied Mathematics and Computation, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A generalization of Pincus’ formula and Toeplitz operator determinants

Archiv der Mathematik, 2003
The author gives a generalization of Pincus' formula. Let \(H\) be a separable Hilbert space and \({\mathcal C}_1(H)\) the set of all trace class operators on \(H\). The main result contains the following Theorem. Let \(A,B \in {\mathcal L} (H),\) and assume that \(AB-BA\in {\mathcal C}_1(H)\).
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The information operator and the asymptotic behavior of the toeplitz determinant

Journal of Soviet Mathematics, 1990
See the review in Zbl 0669.60041.
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A proof of Anđelić-Fonseca conjectures on the determinant of some Toeplitz matrices and their generalization

Linear and Multilinear Algebra, 2022
Yogi Erlangga, Yerlan Amanbek, Bakytzhan Kurmanbek   +2 more
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Toeplitz determinants

1990
Albrecht Böttcher, Bernd Silbermann
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