The SIAM student chapter is starting a faculty lecture series this year with monthly lectures from various faculty members at NCSU. The lectures will be informal introductions to topics in applied mathematics that are typically not taught in classes. It provides a great way to broaden your knowledge of active research topics and engage with professors in the department.
- Wednesday, February 8, 2017 at 4:30 PM in SAS 2229
Arvind Saibaba, NC State
CUR decomposition is a low-rank matrix decomposition that is formed using a small number of actual columns and actual rows of the data matrix. Since this decomposition is explicitly constructed using entries from the actual data set, CUR decomposition may be interpretable by practitioners; for this reason, it is sometimes preferable to the Singular Value Decomposition. I will explain various deterministic and randomized algorithms for computing the CUR decomposition and methods to analyze its accuracy. I will also explain how CUR decomposition can be applied to areas such as recommendation systems, facial recognition and handwriting digit classification.
- Wednesday, March 15, 2017 at 4:30 PM in SAS 2229
Tim Kelley, NC State
Anderson Acceleration: Convergence Theory and Numerical Experience
You’ve probably heard some old guy rant about Newton’s method and how it will solve all of your problems: linear, nonlinear, personal, laundry.
In this talk I’ll tell you about a way to accelerate plain vanilla fixed point iteration. The first theory for this stuff came from right here in SAS hall and there’s much more to do. I’ll tell you some of the theory, explain why you care in the first place, and show you some research opportunities.
- Mansoor Haider, Wednesday April 19 at 4:30 PM in SAS 2229
Exploiting analytical structure to develop accelerated numerical solutions in continuum modeling of materials
In many modeling applications, the analytical structure of fundamental solutions to associated mathematical problems can be exploited to develop more efficient or robust numerical algorithms. I will present several examples of such approaches and techniques based on integral representations arising in the continuum modeling of materials. Some techniques to be discussed include asymptotic analysis, exploiting separability, boundary integral equations and the fast multipole method.
- Wednesday, September 14, 2016 at 4:30 PM in SAS 1108
Alen Alexanderian, NC State
Randomized methods in linear algebra with applications to uncertainty quantification (alensiam16)
Randomized linear algebra is a research area that uses randomization as a computational approach to develop efficient algorithms for large-scale linear algebra problems. In this talk I will discuss randomized methods for computing Singular Value Decomposition (SVD) of matrices, as well as randomized methods for computing trace and determinant of high-dimensional matrices with rapidly decaying eigenvalues. Such matrices are common in scientific computing applications. In addition to some simple illustrations of the randomized methods for test matrices, I will discuss some applications of these methods to problems arising in uncertainty quantification. In particular, we will consider Bayesian linear inverse problems and discuss application of randomized methods for efficient solution methods for such problems. We will also use randomized methods for computation of the log-determinant of the posterior covariance operator, which is an important uncertainty quantification measure in context of Bayesian optimal design of experiments.
- Wednesday, October 26, 2016 at 4:30 PM in SAS 1108
Ralph Smith, NC State
Active Subspace Techniques for Physical, Biological and Financial Models (smithsiam16)
Many physical, biological and financial models contain parameters, initial conditions, or boundary conditions that are not identifiable in the sense that they are not uniquely determined by data. Whereas sensitivity analysis can rank the influence of parameters in many cases, it is generally not effective if parameters are linearly or nonlinear related. In this presentation, we will discuss the construction and use of active subspace techniques to determine subspaces of identifiable or influential parameters. For linear models, this can be achieved using QR or singular value decompositions (SVD), with previously discussed randomized algorithms employed for large input dimensions. For nonlinear models, one typically employs gradients or gradient approximations in combination with QR or SVD techniques. We will illustrate the construction of active subspaces and their use for model calibration through elementary algebraic, ODE and PDE examples. One goal is to illustrate the relevance of active subspace techniques for all graduate students investigating physical, biological, or financial models.
- Wednesday, November 9, 2016 at 4:30 PM in SAS 1108
Pierre Gremaud, NC State
Functional approximation and dimensionality
In this talk, I will discuss both classical and recent results regarding the approximation of functions by simple models such as piecewise constant or any even constant(!) approximations. The emphasis will be on high dimensional problems, i.e., functions of “many” parameters or variables. In particular, we will consider in what way dimensionality, while usually a curse, may also in some limited cases be a blessing.