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Millican lectures are made possible through the generosity of Mr. Olin Moore Millican (1904-1999) who established the Roy McLeod Millican memorial Fund in honor of his brother.

The talks typically take place on Mondays, 4:00-5:00 pm, in GAB 461. The talks are intended for a general audience and everyone is encouraged to attend (including undergraduates). Refreshments are served 30 minutes before the talk in the same room as the talk.

For more information, contact Lea Beneish.

Upcoming Events 

 

2025-9-29 Yingda Cheng, Virginia Tech GAB 461

Low-rank Anderson Acceleration

In this talk, we present the low rank Anderson Acceleration (lrAA), a numerical method that directly computes low rank solutions to nonlinear equations. In many applications (e.g. nonlinear diffusion), the approximate solution, when represented as a matrix, is approximately low rank. It is challenging to design a numerical scheme for nonlinear equations that work directly with low rank. A principal challenge is that if nonlinearities are evaluated element-wise for all matrix elements then the computational savings, from quadratic to linear in the grid points per dimension, is lost.

We propose lrAA, which is based on Anderson Acceleration (AA), a well known technique for accelerating Picard iteration for fixed point problems. We couple AA with low rank truncation and cross approximations. We develop a new method for matrix cross approximation, Cross-DEIM, that uses the discrete empirical interpolation method (DEIM) based index selection to achieve effective cross approximations throughout the iterations. We show that lrAA works well for benchmark problems, such as Bratu problem and Allen-Cahn equations. This is joint work with Daniel Appelö (VT).

Yingda Cheng, a professor at the Department of Mathematics and an affiliated faculty member with the CMDA (Computational Modeling and Data Analytics) program, Virginia Tech. Her research area encompasses scientific computing, applied mathematics, and data-driven modeling and computation. Specifically, she is interested in developing structure-preserving schemes for high-dimensional PDEs. She received a B.S. degree from the University of Science and Technology of China in 2003 and a Ph.D. degree in Applied Mathematics from Brown University in 2007. After a postdoctoral position at the University of Texas at Austin, she was a faculty member at Michigan State University (2011-) before she joined Virginia Tech in 2023. She is a recipient of the SIAM Germund Dahlquist Prize in 2023.

 

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