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 52 for “"Error Bound"”.
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On the Tightness of the Balanced Truncation Error Bound with an Application to Arrowhead Systems
… reduced-order models that satisfy a well-known error bound in terms of a system's Hankel singular values. This bound is known to hold with equality under certain conditions, such as when the full-order system is state-space symmetric. In this work, we derive more general conditions in which the …
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Incremental proper orthogonal decomposition for PDE simulation data: Algorithms and analysis
… and incrementally update both the SVDand an error bound during the time stepping in a PDE solver without storing the simulation data. We show the algorithm produces the exact SVD of an approximate data matrix, and the operator norm error between the approximate and exact data matrices is …
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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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Validation of a Simplified Building Cooling Load Model Using a Complex Computer Simulation Model
… the accuracy of a simplified model to establish error bounds. Having a simplified model and establishing its error bounds, technical estimations from such models could be used in selected applications with more confidence. The error bound relative to DOE-2 predictions, for a proposed simplified …
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Levenberg-Marquardt Algorithms for Nonlinear Equations, Multi-objective Optimization, and Complementarity Problems
… assumption is replaced by a weaker error bound condition. In this way also problems with nonisolated solutions can be treated successfully. Such problems increasingly arise in engineering applications and in mathematical programming. In this thesis we use Levenberg-Marquardt …
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Missing values imputation and image registration for genetics applications
… values using optimal recovery and derive an error bound for non-negative matrix factorization of the imputed data. Second, we consider missing values as erasure channels and show examples of using Fano's inequality to find lower bounds on missing values algorithms. Finally, we perform image …
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A Two-Level Galerkin Reduced Order Model for the Steady Navier-Stokes Equations
… the linearized problem is solved. We prove an error bound for the new 2L-ROM and compare it to the standard Galerkin ROM, or one-level ROM (1L-ROM), in the numerical simulation of the steady Burgers equation. The 2L-ROM significantly decreases (by a factor of 2 and even 3) the 1L-ROM …
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Data-driven decision making in online and offline retail/
… we show an out-of-sample prediction error bound.
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Some aspects of discrete least squares polynomial approximation
… in the discussion of the extended problem, and error bound results. Possible extensions of the programs include the introduction of decision making capabilities so that the user need only specify the data and a tolerance level to achieve a good approximation, and the implementation of the …
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Reduced basis approximation and a posteriori error estimation for non-coercive elliptic problems : applications to acoustics
… in parameter-time space; (ii) a posteriori error estimation - relaxations of the error-residual equation that provide rigorous and sharp bounds for the error in specific outputs of interest; and (iii) offline-online computational procedures - in the offline stage the reduced basis …
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Fundamental limits of wideband localization
… performance measure called the squared position error bound (SPEB) to characterize the localization accuracy. We derive the SPEB succinctly by applying the notion of equivalent Fisher information (EFI). The EFI provides insights into the essence of localization problem by unifying the …
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Hedging Rule for Reservoir Operation: How Much, When and How Long to Hedge
… under hedging, (3) an examination of the error bound between the decision with the actual available forecast and the decision with idea perfect forecast, and (4) an application on a real reservoir operation problem. These are expected to contribute to the understanding of benefits, limits …
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Universal approximation of input-output maps and dynamical systems by neural network architectures
… of the network sufficient to achieve any fixed error tolerance. Furthemore, we show that discrete-time input-output maps given by state-space realizations satisfying certain stability criteria admit such convolutional net approximations which are accurate on an infinite-time scale. For …
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Scalable network localization
… problem that uses the squared position error bound (SPEB) as an objective function. Node Activation controls channel access through the calculation of a optimal binary activation probability. Node Localization is developed in the context of a globally optimum Bayesian estimation problem …
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Autonomous error bounding of position estimates from GPS and Galileo
… important question is whether the navigation error is tolerable. Although differentially corrected GPS is accurate enough for the task most of the time, anomalous measurement errors can create situations where the navigation error is intolerably large. Detection of such situations is referred …
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Model Reduction of Linear Time-Periodic Dynamical Systems
… Additionally, we show an a posteriori error bound written in terms of the $\\mathcal H_2$ norm of related LTI multiple input/multiple output system. This bound inspires an algorithm to construct approximations of reduced order. To verify the efficacy of this algorithm we apply it to …
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Information-theoretic bounds in learning algorithms
… tools to construct performance bounds for the learning algorithms, with the goal of deepening the understanding of current algorithms and inspiring new learning techniques. The first problem considered involves a sequence of machine learning problems that vary in a bounded manner …
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Coupled mode reductions and rotating wave approximations in nonlinear equations
… of the solutions of NLS/GP and analyze the error for the finite dimensional ansatz. Next, we consider a class of discrete nonlinear Klein-Gordon equations with damping and parametric drive. Using small amplitude ansatzs, one usually approximates the equations using a damped, driven discrete …
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Reduced-basis approximation a posteriori error estimation for parabolic partial differential equations
… in parameter-time space; (ii) a posteriori error estimation - relaxations of the error-residual equation that provide rigorous and sharp bounds for the error in specific outputs of interest: the error estimates serve a priori to construct our samples and a posteriori to confirm fidelity; and …
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Reduced-basis output bound methods for parametrized partial differential equations
… Reliability is obtained by a posteriori error estimation methods - relaxations of the standard error-residual equation that provide inexpensive but sharp and rigorous bounds for the error in outputs of interest. Special affine parameter dependence of the differential operator is exploited …
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