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Showing 1 to 20 of 63 for “"Krylov subspace"”.
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Krylov subspace estimation
This thesis proposes a new iterative algorithm for the simultaneous computation of linear least-squares estimates and error variances. There exist many iterative methods for computing only estimates. However, most of these will not also compute error variances. A popular method for computing only …
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Krylov Subspace Methods in Power System Studies
… 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 and the model reduction. Krylov subspace techniques are tested and compared with traditional approaches. …
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Krylov Subspace Spectral Methods with Non-homogenous Boundary Conditions
<p>For this thesis, Krylov Subspace Spectral (KSS) methods, developed by Dr. James Lambers, will be used to solve a one-dimensional, heat equation with non-homogenous boundary conditions. While current methods such as Finite Difference are able to carry out these computations efficiently, their …
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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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Analysis of Dielectric Waveguides and Microstrip Lines Using Krylov Subspace-Based Techniques
… of the algorithm is further improved by using Krylov subspace-based reduction techniques to solve the sparse matrix equation. The numerical technique is also extended to analyze single and multiple discontinuities in the waveguiding structure. Finally, some preliminary work is done on …
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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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Krylov Subspace Spectral Method with Multigrid for a Time-Dependent, Variable-Coefficient Partial Differential Equation
<p>Krylov Subspace Spectral (KSS) methods are traditionally used to solve time-dependent, variable-coefficient PDEs. They are high-order accurate, component-wise methods that are efficient with variable input sizes.</p> <p>This thesis will demonstrate how one can make KSS methods even more …
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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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Stability Analysis of Krylov Subspace Spectral Methods for the 1-D Wave Equation in Inhomogeneous Media
<p>Krylov subspace spectral (KSS) methods are high-order accurate, explicit time-stepping methods for partial differential equations (PDEs) that also possess the stability characteristic of implicit methods. Unlike other time-stepping approaches, KSS methods compute each Fourier coefficient of the …
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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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Iterative Techniques for Radial Basis Function Interpolation
… convergence. The last technique described is a Krylov subspace method which proved to be very successful. It can be applied to any algorithm that fulfils certain criteria. If the underlying algorithm is convergent, the Krylov subspace technique speeds the convergence up. In cases of divergence, …
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Analysis of Acceleration Techniques and Fast Nonlinear Solvers
… 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 formulating both …
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Recycling Preconditioners for Sequences of Linear Systems and Matrix Reordering
… we focus on solving these systems with Krylov subspace methods and how to obtain effective preconditioners inexpensively. We first present an application for electronic structure calculation. A sequence of slowly changing linear systems is produced in the simulation. The linear systems …
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Automatic Construction of Scalable Time-Stepping Methods for Stiff PDES
<p>Krylov Subspace Spectral (KSS) Methods have been demonstrated to be highly scalable time-stepping methods for stiff nonlinear PDEs. However, ensuring this scalability requires analytic computation of frequency-dependent quadrature nodes from the coefficients of the spatial differential operator. …
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Greed, hedging, and acceleration in convex optimization
… We show that, roughly speaking, "most" Krylov-subspace algorithms are asymptotically optimal (in the worst-case) and "most" quadratic functions are asymptotically worst-case functions (for all algorithms). From an algorithmic perspective, this goes against the conventional wisdom that …
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Novel Monte Carlo Methods for Large-Scale Linear Algebra Operations
… a broad family of linear systems, we develop Krylov subspace Monte Carlo solvers that go beyond the use of Neumann series. New algorithms used in the Krylov subspace Monte Carlo solvers include (1) a Breakdown-Free Block Conjugate Gradient algorithm to address the potential rank deficiency …
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Recycling Bi-Lanczos Algorithms: BiCG, CGS, and BiCGSTAB
… introduces recycling BiCG, that recycles the Krylov subspace from one pair of linear systems to the next pair. Augmented bi-Lanczos algorithm and modified two-term recurrence are developed for using the recycle space. Recycle space is built from the approximate invariant subspace corresponding …
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