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 36 for “"rates of convergence"”.
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Rates of Convergence of Continued Fractions and an Approximation Theorem
… Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs
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Weighted and Self-normalized Sums in Free Probability Theory
In this thesis we study the asymptotic behavior of weighted and self-normalized sums in free probability theory and determine the corresponding rates of convergence to their limit distribution.
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Stochastic adaptive system theory for identification, filtering, prediction and control
… thesis examines the basic asymptotic properties of various stochastic adaptive systems for identification, filtering, prediction and control. These include the convergence of long-term averages of signals of interest (self-optimality), the convergence of adaptive filters or controllers …
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Stability Analysis of Time Delay Systems Using Spectral Element Method
<p>The goal of this work is to develop a practical and comprehensive methodology to study the response and the stability of various delay differential equations (DDEs). The development of these new analysis techniques is motivated by the existence of delays in the governing equations of many …
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Statistical aspects of optimal transport
… several statistical problems at the forefront of applied optimal transport, prioritizing statistically and computationally practical results. We begin by considering one of the most popular applications of OT in practice, the barycenter problem, providing dimension-free rates of statistical …
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Numerical solutions for a class of singular integrodifferential equations
… study, we consider numerical schemes for a class of singular integrodifferential equations with a nonatomic difference operator. Our interest in this particular class has been motivated by an application in aeroelasticity. By applying nonconforming finite element methods, we are able to establish …
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Some New Results on Difference Equations of Convolution Type
… verified conditions for asymptotic stability of the zero solution, in terms of the coefficient sequence. Explicit bounds and rates of convergence are considered. We use these results to provide some new bounds for inverses of positive triangular matrices with monotonic column entries. We also …
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Modeling and Estimation of Motion Over Manifolds with Motion Capture Data
Modeling the dynamics of complex multibody systems, such as those representing the motion of animals, can be accomplished through well-established geometric methods. In these formulations, motions take values in certain types of smooth manifolds which are coordinate-free and intrinsic. However, the …
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Density estimation with Kullback-Leibler loss
… density functions are estimated by the method of maximum likelihood in sequences of regular exponential families. The approximation families of log-densities that we consider are polynomials, splines, and trigonometric series. Bounds on the relative entropy (Kullback-Leibler number) between the …
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Mixed methods and reduced integration for the circular arch problem
… include a parameter relating to the thickness of the arch. Existence and uniqueness of solutions to these equivalent problems is established and the corresponding discrete problems are studied. Finite element approximations to the mixed problem are shown to be stable and convergent, and …
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Nonlinear and non-modal stability of structures evolving in shear flows
This thesis explores a range of stability techniques applied to fluid structures that develop in various constant density flows. In particular, the stability of nonlinear structures which develop in rotating plane Couette flow is analyzed using Floquet theory, which allows the global stability of …
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Applications of Stein's method and large deviations principle's in mean-field O(N) models
In the first part of this thesis, we will discuss the classical XY model on complete graph in the mean-field (infinite-vertex) limit. Using theory of large deviations and Stein's method, in particular, Cramér and Sanov-type results, we present a number of results coming from the limit theorems with …
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Wavelet regression with long memory infinite moving average errors
… methods. Among the most successful applications of wavelets is nonparametric statistical estimation, following the pioneering work of Donoho and Johnstone (1994, 1995) and Donoho et al. (1995). In this thesis, we consider the wavelet-based estimators of the mean regression function with long …
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Direct and inverse problems in machine learning
… model under random design with the aim of estimating the unknown target function based on a given set of data, drawn according to some unknown probability distribution. Our estimators are all constructed by kernel methods, which depend on a Reproducing Kernel Hilbert Space structure …
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Statistical inference in two non-standard regression problems
… two parts. The introduction motivates the study of nonstandard problems and presents an outline of the contents of the remaining chapters. In part I, the least squares estimator of a multivariate convex regression function is studied in great detail. The main contribution here is a proof of the …
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A Framework for Grid Solvers
The design and implementation of an object-oriented framework for grid solvers is presented. Unlike conventional sparse solvers, a grid solver solves the sparse linear system embedded in a computational grid without creating the sparse matrix explicitly at any stage of the solution process. This …
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A finite element analysis of high kappa, high field Ginzburg-Landau type model of superconductivity
… is concerned with the formulation and analysis of a simplified GinzburgLandau type model of superconductivity which is valid for large K and large magnetic field strengths. This model, referred to as the High kappa model, is derived via formal asymptotic expansion of the full, time-dependent …
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A Rate of Convergence for Learning Theory with Consensus
… problem with consensus that arises in the study of estimation and control strategies for distributed sensor networks. Each node i for i = 1, . . . , n of the sensor network collects independent and identically distributed local measurements {z i} := {z i j}j∈N := {(x i j , yi j )}j∈N ⊆ X × Y := Z …
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A "HUM" conjugate gradient algorithm for constrained nonlinear optimal control : terminal and regular problems
Optimal control problems often arise in engineering applications when a known desired behavior is to be imposed on a dynamical system. Typically, there is a performance and controller use trade-off that can be quantified as a total cost functional of the state and control histories. Problems stated …
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Learning matrix and functional models in high-dimensions
… data sets. A significant feature of such procedures is that the inferences made are statistically significant, computationally efficient and scientifically meaningful. In this thesis we make several contributions to such statistical procedures. Our contributions are two-fold. We …
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