"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."
| Identifer | oai:union.ndltd.org:wpi.edu/oai:digitalcommons.wpi.edu:etd-dissertations-1403 |
| Date | 24 November 2009 |
| Creators | Ni, Peng |
| Contributors | Homer F. Walker, Advisor, , |
| Publisher | Digital WPI |
| Source Sets | Worcester Polytechnic Institute |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Doctoral Dissertations (All Dissertations, All Years) |
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