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Showing 1 to 20 of 24 for “"Krylov subspace methods"”.
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Krylov Subspace Methods in Power System Studies
… and therefore there is a need to develop new methods for performing these calculations. This study proposes the use of numerical methods based on the Krylov subspace methodology on four areas of power systems: the power flow problem, the dynamic simulation, the trajectory sensitivity analysis …
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Krylov Subspace Methods for Topology Optimization on Adaptive Meshes
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007.
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Strategies For Recycling Krylov Subspace Methods and Bilinear Form Estimation
… of this work is effectiveness and efficiency of Krylov subspace methods and Krylov subspace recycling. While solving long, slowly changing sequences of large linear systems, such as the ones that arise in engineering, there are many issues we need to consider if we want to make the process …
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Krylov subspace methods for simultaneous primal-dual solutions and superconvergent functional estimates
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2002.
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Analysis and Implementation Considerations of Krylov Subspace Methods on Modern Heterogeneous Computing Architectures
Krylov subspace methods are the state-of-the-art iterative algorithms for solving large, sparse systems of equations, which are ubiquitous throughout scientific computing. Even with Krylov methods, these problems are often infeasible to solve on standard workstation computers and must be solved …
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Krylov Subspace Methods with Fixed Memory Requirements: Nearly Hermitian Linear Systems and Subspace Recycling
Krylov subspace iterative methods provide an effective tool for reducing the solution of large linear systems to a size for which a direct solver may be applied. However, the problems of limited storage and speed are still a concern. Therefore, in this dissertation work, we present iterative Krylov …
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Recycling Preconditioners for Sequences of Linear Systems and Matrix Reordering
… to solve linear systems and we always look for methods that are faster and/or require less storage. In this dissertation, we focus on solving these systems with Krylov subspace methods and how to obtain effective preconditioners inexpensively. We first present an application for electronic …
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A new block Krylov subspace framework with applications to functions of matrices acting on multiple vectors
… propose a new framework for understanding block Krylov subspace methods, which hinges on a matrix-valued inner product. We can recast the ``classical" block Krylov methods, such as O'Leary's block conjugate gradients, global methods, and loop-interchange methods, within this framework. Leveraging …
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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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A hybrid direct-iterative linear solver for chemical process simulation
… the reliability of direct sparse linear methods (e.g., Gaussian elimination) with the efficiency of iterative sparse linear methods (e.g., Krylov subspace methods). The new hybrid solver is implemented in the SEQUEL-II, ASPEN PLUS$\sp{\rm TM}$, and SPEEDUP$\sp{\rm TM}$ programs and …
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Preconditioned iterative methods on virtual shared memory machines
… is laid upon how best to optimize iterative Krylov subspace methods using domain decomposition preconditioning. The domain decomposition preconditioner used was developed by J. H. Bramble, J. E. Pasciak, and A. H. Schatz. The Krylov subspace method used was the conjugate gradient algorithm. …
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Analysis of Acceleration Techniques and Fast Nonlinear Solvers
… connections between residual-based acceleration methods and Krylov subspace techniques. The first main contribution is a unified algebraic framework establishing the equivalence between the Anderson Acceleration method and the CROP (Conjugate Residual with Optimal Trial Vector) algorithm. By …
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On the Use of Arnoldi and Golub-Kahan Bases to Solve Nonsymmetric Ill-Posed Inverse Problems
Iterative Krylov subspace methods have proven to be efficient tools for solving linear systems of equations. In the context of ill-posed inverse problems, they tend to exhibit semiconvergence behavior making it difficult detect ``inverted noise" and stop iterations before solutions become …
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ILU and Machine Learning Based Preconditioning For The Discretized Incompressible Navier-Stokes Equations.
… matrices. We consider preconditioned iterative Krylov-subspace methods, such as GMRES, to solve large and sparse linear algebraic systems that result from a Galerkin nite element (FE) discretizations of the linearized Navier-Stokes equations. The corresponding preconditioners are used to …
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Exponential Integrators for the Incompressible Navier-Stokes Equations
… The method is based on a projection onto the subspace of divergence-free (incompressible) functions interleaved with a Krylov-based exponential time integration (KBEI). These time integration methods provide a high order accurate, stable approach with many of the advantages of explicit …
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Multilevel-in-Time Methods for Optimal Control of PDEs and Training of Recurrent Neural Networks
This thesis develops and analyzes “time”-parallel methods for two problem classes: Optimality systems arising in discretized linear-quadratic Partial Differential Equation (PDE)-constrained optimization problems and Recurrent Neural Network (RNN) training problems. While these two problem classes …
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Domain Decomposition Preconditioners for Hermite Collocation Problems
Accelerating the convergence rate of Krylov subspace methods with parallelizable preconditioners is essential for obtaining effective iterative solvers for very large linear systems of equations. Substructuring provides a framework for constructing robust and parallel preconditioners for linear …
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Statistical Preconditioning and Quantitative Imaging for Electrical Impedance Tomography
… are typically the method of choice, with the Krylov subspace methods a frequently used family of iterative schemes. In the case of nonlinear least squares problems, local linearization is an additional step that must be completed before applying an iterative solver. In this thesis, we outline …
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Novel Monte Carlo Methods for Large-Scale Linear Algebra Operations
… to handle large data sets.</p> <p>Monte Carlo methods, which are based on statistical sampling, exhibit many attractive properties in dealing with large volume of datasets, including fast approximated results, memory efficiency, reduced data accesses, natural parallelism, and inherent fault …
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Vibrations in lightweight structures - Efficiency and reduction of numerical models
… extent. Furthermore, the efficiency of different methods for reducing substructure models of multi-storey wood buildings are discussed in the dissertation. Comparisons of different methods for model order reduction, applied to substructures of buildings, showed that the frequently employed method …
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