Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 13 of 13 for “"Krylov Methods"”.
-
Time Integration Methods for Large-scale Scientific Simulations
… require the use of numerical time integration methods to solve. Many problems of scientific interest exhibit stiff behavior for which implicit methods are favorable, however standard implicit methods are computationally expensive. They require the solution of one or more large nonlinear systems …
-
Analysis of the BiCG Method
… Gradient (BiCG) method is an iterative Krylov subspace method that utilizes a 3-term recurrence. BiCG is the basis of several very popular methods, such as BiCGStab. The short recurrence makes BiCG preferable to other Krylov methods because of decreased memory usage and CPU time. …
-
Lightly-Implicit Methods for the Time Integration of Large Applications
… are widely used in the implementation of such methods. The primary focus of this work is on the development of novel ``lightly-implicit'' time integration methodologies. These methods consider the time integration and the solution of the implicit terms as a single computational process. We …
-
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 …
-
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 …
-
Inexact methods for the chemical master equation with constant or time-varying propensities, and application to parameter inference
… that it can be put in the framework of inexact Krylov methods that relax matrix-vector products and compute them expediently by trading accuracy for speed. We also examine practical applications of our work in delay CME and parameter inference through local and global optimization schemes.
-
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 …
-
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 …
-
Accelerated stationary iterative methods for the numerical solution of electromagnetic wave scattering problems
… been much focus on current marching iterative methods, such as Gauss-Seidel and others. These methods attempt to march a solution for the unknown basis function amplitudes in a manner that mimics the physical processes which create the current. In particular the forward backward method has been …
-
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 …
-
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 …
-
Reusing and Updating Preconditioners for Sequences of Matrices
For sequences of related linear systems, the computation of a preconditioner for every system can be expensive. Often a fixed preconditioner is used, but this may not be effective as the matrix changes. This research examines the benefits of both reusing and recycling preconditioners, with special …