ABSTRACT: In this talk, we consider Anderson acceleration with window size $m$ (AA(m)) applied to fixed-point iteration for linear systems. We explore some conditions on the $m+1$ initial guesses of AA(m), aiming for the residuals $r_{m+1}=0$. We propose the sufficient and necessary conditions on the $m+1$ initial guesses for $r_{m+1}=0$. These findings can help us better understand the performance between original fixed-point iteration and Anderson acceleration. Meanwhile, it may give us some guidance on the choice of good initial guesses. Moreover, we give examples to show the temporary stalling behavior of Anderson acceleration applied to solving linear systems.

BIO: Yunhui He is currently an Assistant Professor in the Department of Mathematics at the University of Houston. During 2021-2023 she was a Postdoctoral Research Fellow in the Department of Computer Science at the University of British Columbia. In 2018, She obtained her PhD after three years' study from Memorial University. Following her PhD, she did a one-year postdoc at Memorial University, and then moved to the University of Waterloo for a two-year postdoc.

Her research interests lie in the field of numerical analysis and scientific computing. Specifically, she works on finite element and finite difference methods for the numerical solution of partial differential equations, local Fourier analysis for multigrid methods, and nonlinear acceleration methods such as Anderson acceleration for PDEs and optimization problems.