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Showing 1 to 7 of 7 for “"Nonlinear eigenvalue problems"”.
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Nonlinear eigenvalue problems
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1998.
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Rational Interpolation Methods for Nonlinear Eigenvalue Problems
… thesis investigates the numerical treatment of nonlinear eigenvalue problems. These problems are defined by the condition $T(lambda) v = boldsymbol{0}$, with $T: C to C^{n times n}$, where we seek to compute the scalar-vector pairs, $lambda in C$ and nonzero $ v in C^{n}$. The first contribution …
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Multivariate Rational Approximation in Action: From Data-driven Modeling to Nonlinear Eigenvalue Problems
… by deriving novel formulations of least-squares problems that incorporate interpolation constraints on scattered data sets. Several numerical experiments demonstrate the effectiveness of our proposed algorithms for reduced-order modeling problems and beyond. Further, novel theoretical results …
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Vibrations of mechanical structures: source localization and nonlinear eigenvalue problems for mode calculation
… primary example. I introduce a method of using a nonlinear eigenvalue problem (NLEVP) to express boundary conditions of the vibrating elements so that the (infinitely many) eigenvalues of the full structure are the eigenvalues of the finite-dimensional NLEVP. The mode shapes of the structure can …
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Reduced basis method for quantum models of crystalline solids
Electronic structure problems in solids usually involve repetitive determination of quantities of interest, evaluation of which requires the solution of an underlying partial differential equation. We present in this thesis the application of the reduced basis method in accurate and rapid …
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Extraction of eigen-pairs from beam structures using an exact element based on a continuum formulation and the finite element method
… more precise approximations of higher structure eigenvalues and eigenvectors than are currently available from standard finite elements. The purpose of this study is to investigate hybrid finite element models composed of standard finite elements and exact-elements for the prediction of higher …
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Parametric Dynamical Systems: Transient Analysis and Data Driven Modeling
Dynamical systems are a commonly used and studied tool for simulation, optimization and design. In many applications such as inverse problem, optimal control, shape optimization and uncertainty quantification, those systems typically depend on a parameter. The need for high fidelity in the modeling …