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 40 for “"condition number"”.
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Optimisation of condition number for eigenstructure problems
… eigenvectors by optimising the minimal condition number of the closed-loop eigenvector matrix. This problem is strongly linked to sensitivity of eigenvalues to parameter uncertainty, perturbations to model parameter uncertainty. The importance of this methodology can be expressed in …
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On the explanatory value of condition numbers for convex optimization : theoretical issues and computational experience
The modern theory of condition numbers for convex optimization problems was developed for convex problems in conic format: ... The condition number C(d) for (CPd) has been shown in theory to provide upper and/or lower bounds on many behavioral and computational characteristics of (CPd), from sizes …
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Design and analysis of a Stewart-platform-based six-axis load cell
… loads. Performance can be optimized using the condition number of the transformation matrix. The full-scale version of the hex sensor is also designed and optimized based on its condition number.
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Tetrahedral mesh optimization and generation via topological transformations and gradient based node perturbation
… of the primary optimization metric, weighted condition number. In addition, a thorough literature review regarding tetrahedral mesh generation is given.
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Algebraic approaches for coded caching and distributed computing
… can allow for significant reductions in the number of bits transmitted from the server to the end users. The first part of this dissertation examines problems within coded caching.</p> <p>The original formulation of the coded caching problem assumes that the server and the end users are …
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Visually adaptive virtual sound imaging using loudspeakers
… audio signal processing scheme is limited by the condition number of the associated inversion problem. The condition number as a function of frequency for different listener positions and rotation is examined using an analytical model. The resulting size of the "operational area" with listener …
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Multi-scale problems: an improved non-intrusive algorithm that enhances FEA platforms with the generalized finite element method; An improved preconditioned conjugate gradient solver for hierarchical generalized finite element systems of equations
… the negative effects of machine precision (condition number) in solving GFEM gl systems of equations is called the Stable GFEM gl (SGFEM gl ). This thesis presents results on the ability of SGFEM gl to not only reduce the condition number, but improve solution accuracy over GFEM gl . The …
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Stiffness Analysis of Cable-Driven Parallel Robots
… on stiffness ellipse, directional stiffness and condition number of the stiffness matrix are introduced and calculated and stiffness maps of the robot are developed. In addition, the issue of unit inconsistency in calculating the stiffness index is addressed. One of the areas which is also …
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Quantum Detector and Process Tomography: Algorithm Design and Optimisation
… establish the lower bounds of the UMSE and the condition number for the probe states, and provide concrete examples that can achieve these lower bounds. In order to enhance the estimation precision, we also propose a two-step adaptive QDT and present a sufficient condition on when the infidelity …
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Orthogonality and convergence of discrete Zernike polynomials
… matrix and computationally with the rank and condition number. The convergence of the Fourier-Zernike coe\ufb03cients and the Fourier-Zernike series are also examined using various measures of error. The orthogonality and convergence are studied over six grid types and resolutions, polynomial …
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The Relative Degree of Controllability of Solar Sails in Artificial Lagrangian Orbits
… controllability is determined by comparing the condition number of the controllability Gramian corresponding to individual ALOs. The finite time controllability Gramian is computed for the unstable system, and the magnitude of the individual singular values are used to determine the relative …
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Massively parallel solver for the high-order Galerkin Least-Squares method
… improve the resolution characteristics and the condition number for the high-order interpolation. The Balancing Domain Decomposition by Constraints (BDDC) algorithm is applied to the linear systems arising from the two-dimensional, high-order discretization of the Poisson equation, the …
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A geometric theory of outliers and perturbation
… to a small random relative perturbation has good condition number with high probability, and hence is easy to solve. This is joint work with Avrim Blum, Daniel Spielman, and Shang-Hua Teng. This result forms part of the smoothed analysis project initiated by Spielman and Teng to better explain …
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Smoothed analysis of Gaussian elimination
… A. We prove that it is unlikely that A has large condition number. Using this result, we prove it is unlikely that A has large growth factor under Gaussian elimination without pivoting. By combining these results, we bound the smoothed precision needed to perform Gaussian elimination without …
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On the Complexity of Nonconvex-Strongly-Concave Smooth Minimax Optimization Using First-Order Methods
… level of approximate stationarity and 𝜅 is the condition number, which matches the existing upper bound achieved in (Lin et al., 2020b) up to logarithmic factors. For stochastic oracles, we provide a lower bound of Ω (︀√ 𝜅𝜖⁻² + 𝜅 ¹/³ 𝜖 ⁻⁴)︀ . Second, we study the specific first-order algorithm, …
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Topics in complex random matrices and information theory
… of complex Wishart matrices and the condition number distribution of complex Gaussian random matrices are derived. These distributions are represented by complex hypergeometric functions of matrix arguments, which can be expressed in terms of complex zonal polynomials. We derive …
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Dynamical systems view of acceleration in first order optimization
… the neighborhood can grow larger as the condition number of the function increases. The results altogether provide a systematic way to prove nonasymptotic convergence rates of algorithms derived from ODE discretization.
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Improved approaches to the indirect force determination problems via experimental modal analysis
… content in the response exacerbate the ill-conditioned nature of the indirect-force-determination problem. Numerical techniques for performing the force determination are exploited and compared. The characteristics of the force determination problems are investigated through least squares …
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Quantitative invertibility of random matrices : a combinatorial perspective
… circular law, and the smoothed analysis of the condition number, and our results extend and improve upon theirs in a couple of ways. As opposed to all previous works obtaining such bounds with error rate better than n-1, our proof makes no use either of the inverse Littlewood-Offord theorems, or …
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Robust portfolio construction using sorting signatures
… insights. They relate this angle to the condition number of the covariance matrix and use robust optimisation to improve the conditioning of this matrix. Assuming perfect alpha foresight of an investment manager, we apply a combination of the techniques of Almgren and Chriss (2006) and …
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