Numerical Analysis Seminar
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Date
Time |
Location | Speaker |
Title – click for abstract |
 |
02/19
3:00pm |
BLOC 302 |
David Stewart
University of Iowa |
Ridge Function Machines
Sums of ridge functions $\mathbf{x}\mapsto \varphi(\mathbf{w}^T\mathbf{x})$ can be used to approximate functions ${\mathbb R}^n\to \mathbb R$: $f(\mathbf{x})\approx \sum_{i=1}^m\varphi_i(\mathbf{w}_i^T\mathbf{x})$.
There has been considerable research into how well functions can be approximated in this way.
However, the point of this talk is to describe a way of turning this into a computational method given discrete data points $\{(\mathbf{x}_k,y_k)\mid k = 1,2,\ldots,N\}$. One way of doing this using B-splines is described, which is computationally efficient by iteratively solving a sequence of sparse least squares problems. |
|
02/26
3:00pm |
Zoom |
Ahmad Abassi
University of California Berkeley |
Finite-depth standing water waves: theory, computational algorithms, and rational approximations
We generalize the semi-analytic standing-wave framework of
Schwartz and Whitney (1981) and Amick and Toland (1987) to
finite-depth standing gravity waves. We propose an appropriate
Stokes-expansion ansatz and iterative algorithm to solve the system
of differential equations governing the expansion coefficients. We
then present a more efficient algorithm that allows us to compute the
asymptotic solution to higher orders. Finally, we conclude with
numerical simulations of the algorithms implemented in
multiple-precision arithmetic on a supercomputer to study the effects
of small divisors and the analytic properties of rational
approximations of the computed solutions.
*Joint work with Prof. Jon Wilkening, University of California, Berkeley
Zoom link: https://tamu.zoom.us/j/9415837319 |
The organizer for this seminar is
Bojan Popov.
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