27.11.2013 to 29.11.2013

Michael Tretyakov

University of Nottingham

Michael Tretyakov

10.11.2013 to 23.11.2013

Leonor Cruzeiro

Universidade do Algarve

Leonor Cruzeiro

21.11.2013 to 22.11.2013

Eric Vanden-Eijnden

Courant Institute, NYU

Eric Vanden-Eijnden

13.11.2013 to 15.11.2013

Jeffrey Skolnick

Georgia Tech

Jeffrey Skolnick

17.10.2013

Rob Scheichl

University of Bath

Rob Scheichl

Maxwell-NAIS Seminar on Computational Mathematics (4pm-6pm)

Title: Rigorous Numerical Upscaling of Elliptic Multiscale Problems at High Contrast

Venue: Newhaven Lecture Theatre, ICMS, 15 South College Street, Edinburgh

Abstract: We discuss the possibility of numerical upscaling for elliptic problems with rough diffusion coefficient at high  contrast. Within the general framework of variational multiscale methods, we present a new approach based on novel quasi-interpolation operators with local approximation properties in L2 independent of the contrast. These  quasi-interpolation operators have first been developed in the context and used in the analysis of robust domain decomposition methods. The analysis uses novel weighted Poincare inequalities and an abstract Bramble-Hilbert lemma. We show that for some relevant classes of high-contrast coefficients, optimal convergence without pre asymptotic effects caused by microscopic scales or by the high contrast in the coefficient is possible. Ideas on how to extend the method and the analysis to more general coefficients will be discussed. Classes of coefficients that remain critical are characterized via numerical experiments.

17.10.2013

Folkmar Bornemann

Technische Universitat Munchen

Folkmar Bornemann

Maxwell-NAIS Seminar on Computational Mathematics (4pm-6pm)

Title: The Why and How of Computing Operator Determinants

Venue: Newhaven Lecture Theatre, ICMS, 15 South College Street, Edinburgh

Abstract: The numerical evaluation of operator determinants, originally  meant as an attempt to validate some differential equations calculations for integrable systems, has become a surprisingly useful but simple tool in some areas of Statistics, Mathematical and Theoretical Physics. We review this development, give an introduction to the numerics of operator determinants and explain why equivalent formulations in terms of differential equations are computationally much less useful than previously thought.

09.10.2013

Wolfgang Hackbusch

Max Planck Institut, Leipzig

Wolfgang Hackbusch

Title: Numerical Treatment of Tensors

Venue: EM336, Heriot Watt University, 16:15

Abstract: The numerical treatment of tensors and the use of tensors for various numerical problems has rapidly increased in the recent times. It is now applied to many fields in analysis (treatment of pdes, representation of multivariate functions, etc.) The key for an efficient numerical treatment is a suitable format. We discuss the various formats, their properties, and operations with tensors. The so-called tensorisation even leads to a new concept of discretisations of boundary value problems.

Literature: Wolfgang Hackbush, Tensor spaces and numerical tensor calculus, Springer, 2012. Hackbush is the inventor of the multigrid method.

25.09.2013

Robert Mclachlan

Massey University

Robert Mclachlan

22.08.2013

Professor Marco Cuturi

School of Informatics, Kyoto University

Title: Sinkhorn Distances - Lightspeed Computation of Optimal Transportation Distances

Abstract: Optimal transportation distances are a fundamental family of parameterized distances for probability distributions. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation involves -- when comparing finite dimensional histograms -- the resolution of a linear program whose cost is prohibitive whenever the histograms' dimension exceeds a few hundreds. We propose in this work a new family of optimal transportation distances that look at transportation problems from a maximum-entropy perspective. We smooth the classical optimal transportation problem with an entropic regularization term, and show that the resulting optimum is also a distance which can be computed through Sinkhorn-Knopp's matrix scaling algorithm at a speed that is several orders of magnitude faster than that of transportation solvers. Contrary to traditional network simplex solvers, we show how this algorithm can be vectorized and efficiently parallelized using GPGPUs. We also report improved performance over classical optimal transportation distances on the MNIST benchmark problem. The talk will be self contained and I will spend the first half of the talk introducing the family of optimal transportation distances.

05.08.2013 to 16.08.2013

Juan Bello Rivas

University of Texas

Juan Bello Rivas

Pages