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 12 of 12 for “"symmetric matrix"”.
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Analysis of variance of a randomized block design with missing observations
… This, although requiring the inversion of s symmetric matrix of order equal to the number of missing observations, may prove to be less tedious in application than the iterative method proposed by Yates.
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Graphs, Principal Minors, and Eigenvalue Problems
… processes (DPPs), we consider the classes of symmetric and signed DPPs, respectively, and in both cases connect the problem of learning the parameters of a DPP to a related matrix recovery problem. Next, we consider two conjectures in spectral graph theory regarding the spread of a graph, and …
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A piecewise linear finite element discretization of the diffusion equation
… is a finite volume method that can produce an asymmetric coefficient matrix. We show that the PWL method produces a symmetric positive definite coefficient matrix that can be solved more efficiently, while retaining the accuracy and robustness of Palmer's method. Furthermore, we show that in …
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Secondary Terms in Asymptotics for the Number of Zeros of Quadratic Forms
… over the rational numbers, and let $J$ be the symmetric matrix associated to $F$. One is interested in counting the number of zeros of the quadratic form whose coordinates are restricted in a smoothed box of size $B$. Heath-Brown gave an asymptotic for this question of the form: $c_1 B^{n-2} + …
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Matrix Factorizations, Triadic Matrices, and Modified Cholesky Factorizations for Optimization
… on the Cholesky-related factorizations of symmetric matrices and their application to Newton-type optimization. A matrix is called triadic if it has at most two nonzero off-diagonal elements in each column. Tridiagonal matrices are a special case of these. We prove that the triadic …
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Dendrogram seriation in data visualisation: algorithms and applications
… and measuring anti-Robinson form in a symmetric matrix. This thesis proposes two new seriation criteria, lazy path length and banded anti-Robinson form, and demonstrates their effectiveness in improving a variety of visualisations. The main contribution of this thesis is a new …
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Low rank methods for optimizing clustering
… We utilize low rank structures in the solution matrix of the convex formulation and use a low-rank factorization of the solution matrix directly as a practical alternative. The resulting optimization problem is non-convex, but has a smaller number of solution variables, and can be locally …
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Riemannian geometry of matrix manifolds for Lagrangian uncertainty quantification of stochastic fluid flows
… analyze the embedded geometry of three popular matrix manifolds, namely the fixed rank manifold, the Stiefel manifold and the isospectral manifold. Their extrinsic curvatures are characterized and computed through the study of the Weingarten map. As a spectacular by-product, explicit formulas …
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Numerical simulation of microwave heating of a target with temperature dependent electrical properties in a single-mode cavity
… by this finite-difference approximation has a matrix that is large and non-Hermitian. However, we find that it may be splitted into the sum of a real symmetric matrix and a relatively low-rank matrix. The symmetric system represents the discretization of Helmholtz equation inside an empty and …
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Geometric optimization algorithms for linear regression on fixed-rank matrices
… regression in nonlinear and high-dimensional matrix search spaces. Our purpose is to efficiently exploit the geometric structure of the search space in the design of scalable linear regression algorithms. Our search space of main interest will be the set of low-rank matrices. Learning a …
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The Minimum Rank Problem Over Finite Fields
We have two main results. Our first main result is a sharp bound for the number of vertices in a minimal forbidden subgraph for the graphs having minimum rank at most 3 over the finite field of order 2. We also list all 62 such minimal forbidden subgraphs and show that many of these are minimal …
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D-optymalne chemiczne układy wagowe przy różnych postaciach macierzy kowariancji błędów losowych
W pracy zaprezentowano wyniki dotyczące D-optymalnych chemicznych układów wagowych przy trzech postaciach macierzy kowariancji błędów losowych, które w ogólności są różne od macierzy jednostkowej. W przypadku diagonalnej macierzy kowariancji błędów udowodniono górne oszacowanie wyznacznika macierzy …