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 97 for “"Error bounds"”.
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Error bounds for parallel communication channels.
Thesis: Sc. D., Massachusetts Institute of Technology, Department of Electrical Engineering, 1965
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Surface-surface intersection with validated error bounds
… verified upper bound for the intersection curve error in parameter space. This bound in parametric space is further mapped to an upper bound for the intersection curve error in 3D model space, denoted as model space error, which assists in defining robust boundary representation models of complex …
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Bayesian Estimators, Error Bounds, and Applications to Imaging
… attempts to estimate the physical parameter. The error that accompanies such an estimate is usually characterized by mean squared error (MSE). In a Bayesian setting, the minimum value of the MSE is obtained by the so-called MMSE estimator (MMSEE), which in this sense is the best possible …
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Establishing global error bounds for model reduction in combustion
… To address this issue, this thesis derives bounds on the global error in reduced chemistry models. First, it is shown that many model reduction methods in combustion are based on projection; all of these methods can be described using the same equation. After that, methods from the numerical …
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Accelerated first-order optimization methods using inertia and error bounds
… when the objective function satisfies an error bound which is fairly common in practice, we develop stepsize selections for the subgradient method which significantly outperform the classical approach. The overarching message of this thesis is the following: with careful analysis and …
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ERROR BOUNDS OF COMPACT FINITE DIFFERENCE METHODS FOR SOME DISPERSIVE PDEs AND APPLICATIONS
… system in the subsonic regime. Proofs of error estimate based on energy methods and cut-off techniques are presented, and numerical results are reported for verification purposes. Conservative schemes and schemes with uniform error bounds are considered. Finally, we apply the 4cFD to …
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Interpolants, Error Bounds, and Mathematical Software for Modeling and Predicting Variability in Computer Systems
… with existing approaches. Novel theoretical error bounds are constructed for piecewise linear interpolants over functions with a Lipschitz continuous gradient. Finally, a mathematical software that constructs monotone quintic spline interpolants for distribution approximation from data …
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Error Bounds Between the Minimum Distance Energy of an Equilateral Knot and the Mobius Energy of an Inscribed Smooth Knot
This thesis explores mathematical knots and energy functions defined for them. Specifically, we explore the question of whether or not the Minimum Distance Energy of an equilateral knot is close to the Mobius Energy of a smooth knot where the smooth knot is inscribed in the equilateral knot in a …
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The use and analysis of infinite elements
… and two dimensions, in particular, • to derive error bounds • to show the advantages of the infinite element method • to demonstrate the effectiveness of the error bounds. The realisation of these error bounds depends on a knowledge of the true solution of the problem under examination. However, …
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ERROR ESTIMATES OF NUMERICAL METHODS FOR THE LONG-TIME DYNAMICS OF THE NONLINEAR KLEIN-GORDON EQUATION
This work is devoted to the error estimates of numerical methods for the long-time dynamics of the nonlinear Klein-Gordon equation (NKGE) with weak nonlinearity, which is characterized by $\varepsilon^2$ with $\varepsilon \in (0, 1]$ a dimensionless parameter.The analytical results indicate that …
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Cubature reduction using the theory of inequalities
… two-dimensional integration providing a priori error bounds in a variety of measures of integrand derivatives. Cubature formulae involving both function evaluations and one-dimensional integration are furnished and numerical experiments to investigate the efficacy of the error formulae are …
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Constructive approaches to quasi-Monte Carlo methods for multiple integration
… one popular approach is to study worst-case error bounds in weighted function spaces in which the importance of the variables is moderated by some sequences of weights. Ideally, a family of quasi-Monte Carlo methods in some weighted function space should be strongly tractable. Strong …
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Understanding and Improving Moment Method Scattering Solutions
… problems has been studied by many researchers. Error bounds for the moment method have been obtained in terms of Sobolev norms of the current solution. Motivated by the historical origins of Sobolev spaces as energy spaces, it is shown that the Sobolev norm used in these bounds is equivalent to …
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Topics on option valuation and model calibration
… function is developed. Theoretically, error bounds for bias are explicitly given. Practically, different types of options in commonly used L´evy process models could be priced through this method fast and accurately. Also, sensitivity analysis could be conducted through this approach …
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Born-Oppenheimer Expansion for Diatomic Molecules with Large Angular Momentum
… approximations are used to provide uniform error bounds for the energies of diatomic molecules for bounded vibrational quantum number n and large angular momentum quantum number l. Specifically, results are given when (l + 1) < κ𝛜⁻³/². Explicit formulas for the approximate energies are also …
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Adaptive Stochastic Systems: Estimation, Filtering, And Noise Attenuation
… Squares (LMS), Sign-Regressor (SR), and Sign-Error (SE) algorithms.</p> <p>The analysis is carried out in a multi-scale framework considering the relative size of the gain (rate of adaptation) to the transition rate of the Markovian system parameter. Mean-square error bounds are established, …
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Robust and Data-Efficient Metamodel-Based Approaches for Online Analysis of Time-Dependent Systems
… however, research on how to construct adequate error bounds for GPR-based metamodeling is sparse. Inspired by the challenges encountered in GPR-based analyses of two representative stochastic TDSs, i.e., load forecasting in a power system and trajectory prediction for unmanned aerial vehicles …
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Qualitative and quantitative convergence results for randomised integration methods
… correctness of an algorithm or provide explicit error bounds. The first problem we consider is Lebesgue integration in the unit cube. We prove that a class of structured randomised integration methods is consistent w.r.t. convergence in mean and probability for any integrable function. Under …
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