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Showing 1 to 20 of 120 for “"Krylov"”.
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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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Recycling Krylov Subspaces and Preconditioners
… systems. We develop algorithms that recycle Krylov subspaces and preconditioners from one system (or pair of systems) in the sequence to the next, leading to efficient solutions. Besides the benefit of only having to store few Lanczos vectors, using BiConjugate Gradients (BiCG) to solve dual …
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Krylov Projection Methods for Model Reduction
… dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reduced-order models known as rational interpolants. The cornerstone of this dissertation is a collection of theory relating Krylov projection to rational interpolation. Based on this theoretical framework, three …
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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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Scalable non-blocking Krylov solvers for extreme-scale computing
Krylov solvers are key kernels in many large-scale science and engineering applications for solving sparse linear systems. Extreme-scale systems have many factors that increase communication costs and cause performance variation across cores that can reduce performance at scale. Many Krylov solvers …
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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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Iterative Rational Krylov Algorithm for Unstable Dynamical Systems and Genaralized Coprime Factorizations
… in the original system. The Iterative Rational Krylov Algorithm (IRKA) is a robust model reduction technique which is used to locally reduce stable linear dynamical systems optimally in the ℋ₂-norm. While we cannot guarantee that IRKA reduces an unstable model optimally, there are no numerical …
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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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Hessian Matrix-Free Lagrange-Newton-Krylov-Schur-Schwarz Methods for Elliptic Inverse Problems
… we develop a parallel preconditioned Newton-Krylov method employed in a Hessian-free manner. The preconditioners have an inner-outer structure, taking the form of a Schur complement (block factorization) at the outer level and Schwarz projections at the inner level. However, building an exact …
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GPU and Krylov Based Parallel Model Order Reduction Algorithms for MIMO Circuit Reductions
… Model Order Reduction (MOR) schemes utilizing Krylov Subspace based projections such as the Passive Reduced Interconnect Modeling Algorithm (PRIMA) and Structure-Preserving Reduced-order Interconnect Macromodeling algorithm (SPRIM) have also been widely used. In this thesis, PRIMA and SPRIM …
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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 preconditioned Newton-Krylov method for computing steady-state pulse solutions of mode-locked lasers
… specially preconditioned matrix-implicit Newton-Krylov solver. Solutions are obtained at least an order of magnitude faster than with dynamic simulation, the standard method. Our method is demonstrated experimentally on a one-dimensional temporal model of an eight femtosecond mode-locked laser …
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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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