Please join the Department of Mathematics and Statistics on Thursday, February 3rd at 4:30pm on Microsoft Teams for a fascinating colloquium featuring our very own, Professor Taras Lakoba.
Iterative numerical methods for solving nonlinear equations,and techniques for their acceleration
Taras Lakoba, University of Vermont
Thursday, February 3rd, 4:30pm to 5:30pm, Microsoft Teams
Abstract: This talk will consist of two parts. First, I will review the concept behind iterative methods for obtaining solutions of linear and nonlinear (systems of) equations. One prominent application is finding stationary solitary wave solutions of nonlinear wave equations.
In the second part of the talk, I will consider three techniques to accelerate these methods. The first of these techniques eliminates the numerical stiffness of the system of equations caused by the need to include high Fourier harmonics. The second technique eliminates the slowest-decaying mode in the error of the iterative solution. The third technique is known as the Momentum method in Machine learning and consists of modifying the iterated matrix so as to greatly decrease its condition number.
I will try to make most of the talk accessible to the MS-level graduate and upper-level undergraduate students.
