Title page for ETD etd-112409-140359

Document Type dissertation

Author Name Ni, Peng

URN etd-112409-140359

Title Anderson Acceleration of Fixed-point Iteration with Applications to Electronic Structure Computations

Degree PhD

Department Mathematical Sciences

Advisors
Homer F. Walker, Advisor

Keywords
acceleration
fixed-point

Date of Presentation/Defense 2009-11-13

Availability unrestricted

Abstract
In electronic structure computations, it is necessary to set up and solve a certain nonlinear eigenvalue problem to identify materials. In this dissertation, we first introduce the nonlinear eigenvalue problem and the currently prevailing Self-Consistent Field (SCF) method accelerated by the Anderson acceleration method. We then compare the Anderson acceleration method with the well-known Generalized Minimal Residual (GMRES) method and show that they are essentially equivalent when applied to linear systems. After that, we study a linearly constrained least-squares problem embedded in the Anderson procedure. We use numerical experiments to illustrate the convergence properties. Finally, we give a summary of our work and an outline of future research.

Files
pni.pdf

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Document Type	dissertation
Author Name	Ni, Peng
URN	etd-112409-140359
Title	Anderson Acceleration of Fixed-point Iteration with Applications to Electronic Structure Computations
Degree	PhD
Department	Mathematical Sciences
Advisors	Homer F. Walker, Advisor
Keywords	acceleration fixed-point
Date of Presentation/Defense	2009-11-13
Availability	unrestricted
Abstract In electronic structure computations, it is necessary to set up and solve a certain nonlinear eigenvalue problem to identify materials. In this dissertation, we first introduce the nonlinear eigenvalue problem and the currently prevailing Self-Consistent Field (SCF) method accelerated by the Anderson acceleration method. We then compare the Anderson acceleration method with the well-known Generalized Minimal Residual (GMRES) method and show that they are essentially equivalent when applied to linear systems. After that, we study a linearly constrained least-squares problem embedded in the Anderson procedure. We use numerical experiments to illustrate the convergence properties. Finally, we give a summary of our work and an outline of future research.
Files	pni.pdf