Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 39 for “"toeplitz"”.
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Toeplitz operators
Thesis: M.S., Massachusetts Institute of Technology, Department of Mathematics, 1977
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High-performance algorithms to solve Toeplitz and block Toeplitz matrices
Fast algorithms to factor Toeplitz matrices have existed since the beginning of this century. The two most notable algorithms to factor Toeplitz matrices are the Schur and the Levinson-Durbin. The former factors the Toeolitz matrix itself while the latter factors the inverse. In this thesis, we …
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Algebras of Toeplitz Operators
In this work we examine C*-algebras of Toeplitz operators over the unit ball in ℂ<sup>n</sup> and the unit polydisc in ℂ². Toeplitz operators are interesting examples of non-normal operators that generate non-commutative C*-algebras. Moreover, in the nice cases (depending on the geometry of the …
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An Embedded Toeplitz Problem
In this work we investigate multi-variable Toeplitz operators and their relationship with KK-theory in order to apply this relationship to define and analyze embedded Toeplitz problems. In particular, we study the embedded Toeplitz problem of the unit disk into the unit ball in C^2. The embedding …
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Properties of truncated Toeplitz operators
We discuss the multiplication of truncated Toeplitz operators: or TTOs) on backward shift invariant subspaces of the Hardy space of the unit disc. Specifically we discuss when the product of two TTOs is itself a TTO, finding an equivalent to a similar result of Brown and Halmos for ordinary …
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Isospectral algorithms, Toeplitz matrices and orthogonal polynomials
… of isospectral algorithms, all pertaining to Toeplitz matrices in some fashion, and one directly involving orthogonal polynomials. The first set of algorithms we study come from discretising a continuous isospectral flow designed to converge to a symmetric Toeplitz matrix with prescribed …
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Exploring the Numerical Range of Block Toeplitz Operators
… will explore the numerical range of the block Toeplitz operator with symbol function \(\phi(z)=A_0+zA_1\), where \(A_0, A_1 \in M_2(\mathbb{C})\). A full characterization of the numerical range of this operator proves to be quite difficult and so we will focus on characterizing the boundary of …
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Block Toeplitz operators with rational symbols and discrete singular systems
This thesis concerns block Toeplitz operators (equations). Consider the block Toeplitz operator T = [<I> k-j ]k,j=O' where the <I>k are complex m x m matrices such that 00 (0.1) v=-oo The norm in (0.1) is the usual operator norm on an m x m matrix. The condition (0.1) means that the symbol 00 ( …
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Fast order-recursive Hermitian Toeplitz eigenspace techniques for array processing
… dissertation presents a fast Recursive/Iterative Toeplitz (Hermitian) Eigenspace (RITE) algorithm, and its extension to the generalized strongly regular eigendecomposition situation (C-RITE). Both procedures exhibit highly parallel structures, and their applicability to fast passive array …
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Structured linear algebra problems and applications to system identification
… of the broad class of positive definite Toeplitz-like matrices is given. For nearly semidefinite Toeplitz matrices, it is proven that the Cholesky factor has a limited rank-revealing property. This property has a close connection with a stability result for the Schur algorithm for the …
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Banded matrices with banded inverses
… We perform this factorization on both the Toeplitz and non-Toeplitz case for the two factor case, while we do it only for the Toeplitz case in the three factor case. We then look at extending our results when the banded matrix has elements at its corners. We show that this case is not very …
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A fast characteristic finite difference method for fractional advection-diffusion equations with non-linear reaction.
… the advection-diffusion equation utilizing fast Toeplitz matrix-vector multiplication. We then extend the method to the two-dimensional case. Numerical results are provided to compare performance of the methods proposed.
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Quantum stochastic flows on universal partial isometry matrix C*-algebras
… Included in the isometry *-bialgebras is the Toeplitz algebra; we also examine this very closely. We investigate how Levy processes on the Toeplitz algebra act on its commutative sub-C*-algebras. To motivate the noncommutative setting we also consider classical Markov chains in terms of …
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Detection of multiple correlated time series and its application in synthetic aperture sonar imagery
… the true GLRT for this problem would impose a Toeplitz structure (more specifically, a Toeplitz-block-Toeplitz structure) on the estimate of the composite covariance matrix, an intractable problem with no closed-form solution, the asymptotic theory of large Toeplitz matrices shows that the …
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Low-rank completion and recovery of correlation matrices
… performed on the classical exponential and noisy Toeplitz parametrisations and, in addition, to real datasets comprising of FX rates and stock price data. In almost all instances, the method of convex relaxation performed better than spectral methods and achieved the closest and best-fitted …
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Multiphysics Design and Modeling for Advanced Packaging and Heterogeneous Integration of Power Delivery
… approach with Fourier series–based Toeplitz matrices. This method provides a unified framework for transient electrical simulations and steady-state thermo-mechanical analysis, representing time-varying system elements in the frequency domain to improve stability and efficiency. To …
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Operators and special functions in random matrix theory
… be expressed as the sum of a Hankel square and a Toeplitz operator.
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A fast 3D full-wave solver for nanophotonics
… and solve a linear system. Moreover, the block Toeplitz matrix property and using FFT helps reduce memory requirement, and accelerate the circulant matrix vector product. Numerical experiments are presented to demonstrate that this method can effectively reduce reflections to 1%, and is easily …
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Difference-operator-based models in statistical signal processing
… model involves solving a non-Toeplitz system of linear equations. We derive an algorithm for efficiently estimating these parameters, analogous to the Levinson algorithm for conventional models. Numerical results have been obtained that indicate that, in the presence of …
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Electromagnetic scattering and induction models for spheroidal geometries
… quickly evaluated using a novel multilevel block-Toeplitz matrix vector multiply based on the Fast Fourier Transform.
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