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PhD Exit Seminar: Convergence Analysis of Alternating Anderson-Picard Method for Nonlinear fixed-point Problem
Special Events| Speaker: | Xue Feng |
| Location: | 2112 MSB |
| Start time: | Tue, Jun 4 2024, 4:10PM |
Anderson Acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This work considers a variant where Anderson Acceleration and Picard iteration are alternated, known as the Alternating Anderson-Picard (AAP) method. This method capitalizes on the efficiency of AA in speeding up convergence and the simplicity of Picard iterations to generate historical points at each AA step. We study the convergence properties of AAP. The core is to establish the equivalence between AAP method and the Multisecant-GMRES method, which is closely related to the Newton-GMRES method. This equivalence also helps to bound the optimization gain, a concept crucial in quantifying AA's convergence rate, yet its implications have not been fully understood. Only a basic understanding of numerical optimization is required to follow my talk, so welcome to join!
HYBRID: Join Zoom Meeting https://ucdavis.zoom.us/j/97925010008?pwd=VUk4K0k0dXNPUHA0blJxUUFlUGlNZz09 Meeting ID: 979 2501 0008 Passcode: 437440