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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 143 for “"eigenvectors"”.
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Optimizing and approximating eigenvectors in max-algebra
This thesis is a reflection of my research in max-algebra. The idea of max-algebra is replacing the conventional pairs of operations (+,x) by (max, +). It has been known for some time that max-algebraic linear systems and eigenvalue-eigenvector problem can be used to describe industrial processes …
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On eigenvectors for semisimple elements in actions of algebraic groups
… $E$ denote the set of vectors in $V$ which are eigenvectors for some non-central semisimple element of $G$ and some eigenvalue in $K^∗$. We prove, with a short list of possible exceptions, that the dimension of $\overline{E}$ is strictly less than the dimension of $V$ provided $\dim V > \dim G + …
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Eigenvalues and low energy eigenvectors of quantum many-body systems
I first give an overview of the thesis and Matrix Product States (MPS) representation of quantum spin systems on a line with an improvement on the notation. The rest of this thesis is divided into two parts. The first part is devoted to eigenvalues of quantum many-body systems (QMBS). I introduce …
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Two Random Multiplicative Processes: Multiplicative Cascades and Eigenvectors of the Random Schrodinger Operator
… measures.In the second chapter, we focus on the eigenvectors of the one-dimensional discrete random Schrodinger operator. This is the Hamiltonian operator on the lattice of integers given by the discrete Laplacian plus an independent, identically distributed delta potential at each point. We …
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Gauss elimination operator for determining the characteristic poplynomial and eigenvectors of any square matrix
Digitized by Kansas Correctional Industries
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Correlations between MO Eigenvectors and the Thermochemistry of Simple Organic Molecules, Related to Empirical Bond Additivity Schemes
A bondingness term is further developed to aid in heat of formation (ΔfHº) calculations for C, N, O and S containing molecules. Bondingness originated from qualitative investigations into the antibonding effect in the occupied MOs of ethane. Previous work used a single parameter for bondingness to …
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Restarting the Lanczos algorithm for large eigenvalue problems and linear equations.
We are interested in computing eigenvalues and eigenvectors of large matrices and in solving large systems of linear equations. Restarted versions of both the symmetric and nonsymmetric Lanczos algorithms are given. For the symmetric case, we give a method called Lan-DR that simultaneously solves …
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Neural Networks on Eigenvector Data
The need to process eigenvectors derived from data arises across numerous domains in computing and the sciences. However, eigenvectors differ from other types of data, as they have particular symmetries; for any eigenvector of a matrix, the negation of that vector is also an eigenvector of the same …
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Free approximation of transport properties in organic system using Stochastic Random Matrix Theory
… probability, conductivity and etc. Due to the eigenvectors' shifts, RMT works well only for small disorder. System with larger disorder requires to take in account of the changes in eigenvectors directly or through other approximations of the eigenvectors.
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A generalized approach for calculation of the eigenvector sensitivity for various eigenvector normalizations
… the eigenvector sensitivity for mass normalized eigenvectors only. A new generalized method is presented to calculate the first and second order eigenvector sensitivities for eigenvectors with any normalization condition. This new generalized method incorporates the use of normalization condition …
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Learning Sparse Graph Laplacian with K Eigenvector Prior via Iterative GLASSO and Projection
… Laplacian matrix is considered: the first K eigenvectors of the graph Laplacian are pre-selected, e.g., based on domain-specific criteria, and the remaining eigenvectors are then learned from data. One example use case is image coding, where the first eigenvector is pre-chosen to be constant, …
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New feedback design methodologies for large space structures: a multi-criterion optimization approach
… in regards to conditioning (robustness) of the eigenvectors. Finally, to illustrate the ideas presented in this study, we adopt numerical examples in two sets: 1) 6th order mass-spring systems and 11) various reduced order models of a flexible system. The numerical results confirm that …
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Schrödinger equation with periodic potentials.
… is reduced to the problem of finding the eigenvectors of an infinite matrix. The infinite matrix is truncated to a finite matrix. The approximation due to the truncation is carefully studied. The band structure of the eigenvalues is shown. The eigenvectors of the multiwells potential are …
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Spectral properties of the random conductance model
… a large box, is intimately linked to the first eigenvectors and eigenvalues of its generator with zero Dirichlet boundary condition. This follows directly from the spectral decomposition of the associated heat equation. In this thesis, we study these first eigenvectors and eigenvalues when the …
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Perturbation methods for slightly damped gyroscopic systems
… is to express the perturbed eigenvalues and eigenvectors in terms of the unperturbed eigenvalues and eigenvectors and the perturbing matrices, without solving a new eigenvalue problem. If all of the unperturbed eigenvalues are clearly distinct, which is to say that the difference between no …
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Spectrum of some regular graphs with widely spaced modifications
… show that by applying those modifications, new eigenvectors that are localized near the components that correspond to the modified rows appear. By knowing the approximate form of those eigenvectors, we also determine a very close (and simple) approximation to the eigenvalues, and then we show …
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Computation of nodes and weights of Gaussian Quadrature rule by using Jacobi method
… of Gaussian quadrature and eigenvalues and eigenvectors. Thus the need for faster methods to solve these larger eigenvalue problems has become very important. A standard textbook method for finding the eigenvalues of a matrix A is to solve for the roots of \lambda It is quite easy to solve …
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Data Assimilation and Applications in Forecasting
… covariance matrix through the estimation of eigenvectors. Specifically, we estimate the leading large-scale eigenvectors from a sample covari- ance matrix calculated from a spatially smoothed ensemble with spatial localization applied with a long localization distance. We then create …
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Reduced basis method for quantum models of crystalline solids
… eigensolutions - solutions consisting of several eigenvectors. The first strategy exploits the optimality of the Galerkin procedure to find a solution in the span of all eigenvectors at N judiciously chosen samples in the parameter space.
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