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Showing 1 to 18 of 18 for “"Arnoldi"”.
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Convergence of the Arnoldi Iteration for Estimating Extreme Eigenvalues
Krylov subspace methods, like the Arnoldi iteration, are a powerful tool for efficiently solving high-dimensional linear algebra problems. In this work, we analyze the convergence of Krylov methods for estimating the numerical range of a matrix. Prior bounds on approximation error often depend on …
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On the Use of Arnoldi and Golub-Kahan Bases to Solve Nonsymmetric Ill-Posed Inverse Problems
… in the orthonormal basis generated by the Arnoldi process (which is fundamental to the popular iterative method GMRES) has been of renewed interest recently. We discuss some of the positive and negative aspects of each process and use example problems to examine some qualities of the bases …
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Efficient Solution of Large Sparse Eigenvalue Problems in Microelectronic Simulation
We present a new Chebyshev-Arnoldi algorithm for finding the lowest energy eigen-functions of an elliptic operator. The algorithm, which is essentially the same for symmetric, nonsymmetric, and complex nonhermitian matrices, is adapted to a specific problem by two subroutines which encapsulate the …
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Model order reduction of electro-thermal MEMS
… model order reduction (MOR) methods (preferably Arnoldi algorithm) to the automatic generation of accurate dynamic compact thermal models (DCTM) of electro-thermal microsystems. Unlike conventional approaches to DCTM, which are based on the lumped-element decomposition of the model followed by …
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Model order reduction for nonlinear systems
… and tensor reduction with assistance of Arnoldi type projection, we demonstrate a much better accuracy for the reduced nonlinear system to capture the original behavior than the traditional linearization method.
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A Paradigm Shift in African Cultural Exhibits at the National Museum of Natural History
… the Smithsonian, anthropology curator, Mary Jo Arnoldi stated that the 1967 Cultures of Africa exhibit in the National Museum of Natural History was outdated the day it opened. I examine how curators’ reluctance to abandon 19th century evolution theories for this 1967 exhibition, may have …
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Restarting the Lanczos algorithm for large eigenvalue problems and linear equations.
… We also investigate a restarted two-sided Arnoldi. We compare expense and stability of this approach with restarted nonsymmetric Lanczos.
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Three Dimensional Pseudospectral Self -Consistent Field Approximation
… of Davidson's method, or spectrally localized Arnoldi's method, is used. The full-size problem is projected onto Krylov subspaces of limited size with an explicitly orthogonalized basis. The smaller-size projected problem is solved using LAPACK library functions and then the solution is …
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Krylov Projection Methods for Model Reduction
… are proposed. The first algorithm, dual rational Arnoldi, is a numerically reliable approach involving orthogonal projection matrices. The second, rational Lanczos, is an efficient generalization of existing Lanczos-based methods. The third, rational power Krylov, avoids orthogonalization and is …
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Model-order reduction techniques for the numerical solution of electromagnetic wave scattering problems
… formulation of an approximate extension of the Arnoldi algorithm to produce a ROM for an inhomogeneous contrast-sweep and source-sweep analysis. ² Investigation of the application of the Well-Conditioned Asymptotic Waveform Evaluation (WCAWE) technique to problems in which the system matrix has …
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Stochastic analyses of mechanical and biomedical structures with uncertainties
… For deterministic model order reduction, the Arnoldi-based Krylov subspace technique is implemented to reduce the system matrices of the finite element model. In the stochastic model order reduction, the stochastic reduced basis method is implemented in which the modal and frequency responses …
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Some studies on the computation and interpretation of seismic interface waves and modes in Earth’s mantle
… problem, which I solve with the Infinite Arnoldi method. I explore the oscillation modes of simple mechanical systems, and show how more complicated rheologies, such as the Extended Burgers model, can be handled, with comparisons to previous work. I conclude by discussing applications on …
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Traditional and modern carved doors as a manifestation of Yoruba culture
Thesis (M.S.)--Michigan State University. Dept. of Art, 1975
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Reduced-order aerodynamic models for aeroelastic control of turbomachines
… for turbomachinery which is based on computing Arnoldi vectors. This method matches the input/output characteristic of the CFD model and includes the proper orthogonal decomposition as a special case. Here, reduction is applied to the linearized two-dimensional Euler equations, although the …
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Time Integration Methods for Large-scale Scientific Simulations
… Rosenbrock-Krylov methods which replace the Arnoldi iteration used to produce the Krylov approximation with Lanczos biorthogonalization, which requires fewer vector dot products, leading to lower overall cost for stiff problems. Linearly implicit multistep methods are a new family of implicit …
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Recycling Preconditioners for Sequences of Linear Systems and Matrix Reordering
… GCROT and recycling, we use information from an Arnoldi recurrence to determine which directions to keep. We investigate and analyze their properties. We also prove that both truncation approaches work well under suitable conditions. We apply our truncation approaches on two applications. One is …
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Moment Matching and Modal Truncation for Linear Systems
While moment matching can effectively reduce the dimension of a linear, time-invariant system, it can simultaneously fail to improve the stable time-step for the forward Euler scheme. In the context of a semi-discrete heat equation with spatially smooth forcing, the high frequency modes are …