Worcester Polytechnic Institute Electronic Theses and Dissertations Collection

Title page for ETD etd-112409-140359


Document Typedissertation
Author NameNi, Peng
URNetd-112409-140359
TitleAnderson Acceleration of Fixed-point Iteration with Applications to Electronic Structure Computations
DegreePhD
DepartmentMathematical Sciences
Advisors
  • Homer F. Walker, Advisor
  • Keywords
  • acceleration
  • fixed-point
  • Date of Presentation/Defense2009-11-13
    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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