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Sayas Numerics Seminar

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SAYAS NUMERICS SEMINAR is a weekly online seminar in Fall 2020 on computational mathematics organized by the mathematics departments of

·         University of Maryland, College Park

·         University of Maryland, Baltimore County

·         George Mason University

·         University of Delaware

Talks will take place via Zoom on Tuesdays at 3:30 PM Eastern Time. Pre-registration is necessary to attend. 

For a list of talks, registration page and more information see:

https://sayasseminar.math.umd.edu

The seminar series welcomes contributed talks from students, early career researchers and post-docs.  See the above page for details (submission of contributed talks deadline: Sept 7).


 

 

Tamara G. Kolda (Sandia National Laboratories)Tamara G. Kolda (Sandia National Laboratories)Zoom: register @ http://www.udel.edu/007661<br>Title: Practical Leverage-Based Sampling for Low-Rank Tensor Decomposition <br> <br>Abstract: Conventional algorithms for finding low-rank canonical polyadic (CP) tensor decompositions are unwieldy for large sparse tensors. The CP decomposition can be computed by solving a sequence of overdetermined least problems with special Khatri-Rao structure. In this work, we present an application of randomized algorithms to fitting the CP decomposition of sparse tensors, solving a significantly smaller sampled least squares problem at each iteration with probabilistic guarantees on the approximation errors. Prior work has shown that sketching is effective in the dense case, but the prior approach cannot be applied to the sparse case because a fast Johnson-Lindenstrauss transform (e.g., using a fast Fourier transform) must be applied in each mode, causing the sparse tensor to become dense. Instead, we perform sketching through leverage score sampling, crucially relying on the fact that the structure of the Khatri-Rao product allows sampling from overestimates of the leverage scores without forming the full product or the corresponding probabilities. Naive application of leverage score sampling is ineffective because we often have cases where a few scores are quite large, so we propose a novel hybrid of deterministic and random leverage-score sampling which consistently yields improved fits. Numerical results on real-world large-scale tensors show the method is significantly faster than competing methods without sacrificing accuracy. This is joint work with Brett Larsen, Stanford University. <br>10/6/2020 7:30:00 PM10/6/2020 8:30:00 PMFalse
Lars Ruthotto (Emory University)Lars Ruthotto (Emory University)Zoom: register @ http://www.udel.edu/007661<br>Title: TBA <br> <br>Abstract: TBA <br>10/13/2020 7:30:00 PM10/13/2020 8:30:00 PMFalse
Akil Narayan (University of Utah)Akil Narayan (University of Utah)Zoom: register @ http://www.udel.edu/007661<br>Title: Multivariate positive quadrature rules and computational Tchakaloff theorems <br> <br>Abstract: The design of interpolatory quadrature rules with positive weights is of great interest in approximation theory and scientific computing: Such quadrature rules achieve near-optimal approximation of integrals and are associated with well-behaved Lebesgue constants. Such quadrature rules are used heavily in applications like uncertainty quantification and computational finance. Computing such quadrature rules in more than one dimension is an arduous task, frequently attempted with non-convex optimization schemes. The success or failure of such approaches typically depends on the type of domain, dimension, or approximation space. We present a new procedure whose implementation is a probabilistic algorithm based on a novel constructive proof of Tchakaloff's theorem. In particular, we can successfully compute size-N quadrature rules in high dimensions for general approximation spaces. The main feature of our algorithm is a complexity that depends algebraically on N, and in some cases is strictly linear in the dimension. We illustrate that our procedure is effective even for quadrature on complex and unbounded multivariate domains. <br>10/27/2020 7:30:00 PM10/27/2020 8:30:00 PMFalse
Denis Ridzal (Sandia National Laboratories)Denis Ridzal (Sandia National Laboratories)Zoom: register @ http://www.udel.edu/007661<br>Title: TBA <br> <br>Abstract: TBA <br>11/3/2020 8:30:00 PM11/3/2020 9:30:00 PMFalse

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  • Department of Mathematical Sciences
  • University of Delaware
  • 501 Ewing Hall
  • Newark, DE 19716, USA
  • Phone: 302-831-2653
  • math-questions@udel.edu