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
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.
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