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 27 for “"least squares problem"”.
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Estimation of the In-Cylinder Air/Fuel Ratio of an Internal Combustion Engine by the Use of Pressure Sensors
… exponent. The first method results in a linear least-squares problem, and the second method results in a nonlinear least-squares problem. The nonlinear least-squares problem is solved by separating out the nonlinear dependence and solving the single-variable minimization problem. For this, a …
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Model identification with application to building control and fault detection
… may still be solved as an unconstrained linear least squares problem. To enforce the constraint on system eigenvalues, the problem is formulated as an unconstrained mixed (linear and non-linear) least-squares problem, which is easier to solve than the corresponding problem with linear objective …
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Motion modeling and video processing
… of MA filtering) to the solution of a weighted least squares problem. This least squares problem is then generalized to enable modeling (filtering) of motion fields. Our AR model for motion is significantly different from previous approaches in that instead of computing motion at a pixel as a …
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The Sherman Morrison Iteration
… method is developed to solve regularized least squares problems. Notions of pivoting and splitting are deliberated on to make the method more robust. The Sherman Morrison iteration method is shown to be effective when dealing with an extremely underdetermined least squares problem. The …
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Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS)
This thesis develops the Non-Intrusive Least Squares Shadowing (NILSS) method, which computes the sensitivity for long-time averaged objectives in chaotic dynamical systems. In NILSS, we represent a tangent solution by a linear combination of one inhomogeneous tangent solution and several …
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Structured Sparsity Promoting Functions: Theory and Applications
… the effect of these functions on the penalized least squares problem and discuss several algorithms for solving this problem which rely on the particular structure of our functions. We then apply these methods to the total variation denoising problem from signal processing.</p>
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Parallel Gauss-Newton method for CP decomposition
… architectures and comparative to Alternating least squares algorithm for CP decomposition. Alternating least squares may exhibit slow or no convergence, especially when high accuracy is required. CP decomposition problem can be formulated as a non-linear least squares problem to apply …
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Row-Action Methods for Massive Inverse Problems
… have seen the rise of massive inverse problems, where there are too much data to implement an all-at-once strategy to compute a solution. Additionally, tools for regularizing ill-posed inverse problems are infeasible when the problem is too large. This thesis focuses on the development …
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Optimization Based Domain Decomposition Methods for Linear and Nonlinear Problems
… crux of the method is a constrained minimization problem for which the objective functional measures the jump in the dependent variables across the common boundaries between subdomains; the constraints are the partial differential equations. First, we consider a linear constraint. The existence of …
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A robust optimization approach to statistical estimation problems by Apostolos G. Fertis.
… by applying robust optimization to the classical least squares problem. We discover the explicit connection between the size and the structure of the uncertainty set used in the robust estimator, with the coefficient and the kind of norm used in regularization. We compare the out-of-sample …
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Dynamic estimation of origin-destination trip-tables from real-time traffic volumes using parameter optimization methods
… Two models have been developed for this problem, one based on a least squares estimation and the other based on an <i>1</i>₁ norm approach. Two projected conjugate gradient schemes are investigated for solving the constrained least squares problem, and an interior point affine scaling …
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Numerical methods for optimization problems in water flow and reactive solute transport processes of xenobiotics in soils
… fields: 1. Modeling of parameter estimation problems and optimal experimental design problems: Mathematical modeling of water and solute transport processes in the unsaturated zone leads to instationary partial differential equations (PDEs) coupled with nonlinear ordinary differential …
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Advanced modeling and computational methods for distribution system state estimation
… rely on iterative methods to solve the weighted least squares problem because of the nonlinear relationship between the power measurements and voltage phasor state. It is known that these methods may be prone to convergence and numeric instability issues, such as in the presence of a measurement …
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Statistical learning with differential privacy
… privacy and utility is crucial for effective problem-solving in data science. This dissertation addresses the challenge by proposing methodologies for statistical learning tasks while upholding privacy principles. The tasks include (1) constructing private confidence intervals for population …
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Geometrically-informed methods of wave-based imaging
… context of full-waveform inversion, a non-linear least-squares problem for estimating material properties within the domain of interest. We analyze the contributions of reflected and transmitted waves to the linearized Hessian operator, demonstrating that reflected waves generally produce a …
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Compound-Gaussian-regularized inverse problems: theory, algorithms, and neural networks
Linear inverse problems are frequently encountered in a variety of applications including compressive sensing, radar, sonar, medical, and tomographic imaging. Model-based and data-driven methods are two prevalent classes of approaches used to solve linear inverse problems. Model-based methods …
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Control Theoretic Methods In Analysis And Design Of Optimization Algorithms
… for solving a class of convex optimization problems with time-varying objective and constraint functions. This dynamical system is composed of two terms: (i) a correction term consisting of a continuous-time version of Newton's method, and (ii) a prediction term able to track the drift of …
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Numerical Methods for Parameter Estimation and Optimal Control of the Red River Network
… does not work effectively. To overcome this problem and to come up with accurate parameter values, we estimate these parameters by solving a corresponding least-squares problem. This high dimensional nonlinear constrained optimization problem is solved by applying a special reduced …
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Risk Assessment and Optimal Response Strategies for Resilience of Electric Power Infrastructure to Extreme Weather
… are estimated using a Constrained Nonlinear Least Squares problem. Inclusion of asymmetries in the model improves the accuracy of wind risk assessment in the hurricane eye wall, where wind velocities are maximized. Secondly, the wind field forecasts are used as inputs to a probabilistic model …
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Stretched Exponential Decline Model as a Probabilistic and Deterministic Tool for Production Forecasting and Reserve Estimation in Oil and Gas Shales
… parameters, can be determined by the method of least squares in various ways, but the inherent nonlinear character of the least squares problem cannot be bypassed. To assure a unique solution to the parameter estimation problem, this work suggests a physics-based regularization approach, based …
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