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Colloquium: Prof. Hans De Sterck

Event Type: 
Colloquium
Speaker: 
Prof. Hans De Sterck
Event Date: 
Tuesday, April 27, 2021 -
3:30pm to 4:45pm
Location: 
Zoom: https://unm.zoom.us/j/91525130869
Audience: 
Faculty/StaffStudents

Event Description: 

https://unm.zoom.us/j/91525130869

Title:
Convergence Acceleration for Nonlinear Fixed-Point Methods

Abstract:
Empirical results show that nonlinear convergence acceleration methods such as Anderson Acceleration (AA) or the Nonlinear Generalized Minimal Residual (NGMRES) method may often dramatically speed up the convergence of fixed-point algorithms that are widely used in scientific computing and optimization. However, little is known theoretically that can help us to understand and quantify the asymptotic convergence improvement. We present new results that shed light on this open problem, by considering optimal stationary versions of the acceleration methods that allow us to quantify the convergence improvement using spectral properties of the Jacobian of the fixed-point iteration function, viewed as a nonlinear preconditioner. We illustrate these findings for nonlinear acceleration of the Alternating Least Squares (ALS) method for tensor decomposition, and the Alternating Direction Method of Multipliers (ADMM) for optimization problems in machine learning.

 

Event Contact

Contact Name: Jacob Schroder

Contact Email: jbschroder@unm.edu