[Todos CMAT] Conferencia R. Tempone. Miércoles 24/14 horas/Cmat

[Ernesto Mordecki]

Hola a todos, el* Miércoles 24 a las 14 horas en el salón del piso*
*15 del CMAT*, invitamos a la charla de *Raúl Tempone*
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Title: Multilevel weighted least squares polynomial approximation

Abstract:
We propose and analyze a multilevel weighted least squares polynomial
approximation method. Weighted least squares polynomial approximation uses
random samples to determine projections of functions onto spaces of
polynomials. Using an optimal distribution of sample locations, the number
of samples required to achieve quasi-optimal approximation in a given
polynomial subspace scales, up to a logarithmic factor, linearly in the
dimension of this space. However, in many applications, the computation of
samples includes a numerical discretization error. Thus, obtaining
polynomial approximations with a single level method can become
prohibitively expensive, as it requires a sufficiently large number of
samples, each computed with a reasonably small discretization error. As a
solution to this problem, we propose a multilevel method that utilizes
samples computed with different accuracies and can match the accuracy of
single-level approximations with reduced computational cost. We derive
complexity bounds under certain assumptions about polynomial
approximability and sample work. Furthermore, we propose an adaptive
algorithm for situations where such assumptions cannot be verified a
priori. Finally, we provide an efficient algorithm for the sampling from
optimal distributions and an analysis of computationally favorable
alternative distributions. Numerical experiments illustrate the
applicability of our method.

References:

 "Multilevel weighted least squares polynomial approximation," by A.-L.
Haji-Ali, F. Nobile, R. Tempone and S. Wolfers. ArXiv:1707.00026, June 2017.
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Shortest Bio  Aquí
<https://www.dropbox.com/s/jjhdzsjnopduip9/_DSC9749-x.jpg?dl=0> una foto de
Raúl
Raúl Tempone graduated as an industrial engineer in 1995 from the
University of the Republic, Montevideo, Uruguay. After graduation, he
worked on the optimal dispatch of electricity for the Uruguayan system
using techniques from nonlinear stochastic programming and visited the
Royal Institute of Technology (KTH) in Stockholm, Sweden, to study
numerical analysis. He obtained a Master in Engineering Mathematics in 1999
(inverse problems for incompressible flows, supervised by Jesper
Oppelstrup, KTH) and a Ph.D. in Numerical Analysis in 2002 (a posteriori
error estimation and control for stochastic differential equations,
supervised by Anders Szepessy, KTH). He later moved to ICES, UT Austin, to
work as a postdoctoral fellow from 2003 until 2005 in the area of numerical
methods for PDEs with random coefficients (supervised by Ivo Babuska and
Mary Wheeler). In 2005 he became an assistant professor (joint appointment)
with the School of Computational Sciences and the Department of Mathematics
at Florida State University, Tallahassee. In 2007 he was awarded the first
Dahlquist fellowship by KTH and COMSOL for his contributions to the field
of numerical approximation of deterministic and stochastic differential
equations. In 2009 he joined King Abdullah University of Science and
Technology as Associate Professor (founding faculty) and was promoted in
2015 to the rank of Full Professor in Applied Mathematics. Since 2012, he
has been directing the KAUST Strategic Research Center for Uncertainty
Quantification. In May 2018, he has been recently awarded an Alexander von
Humboldt Professorship (hosted  by RWTH Aachen) by the German Ministry of
Education and Research.

-- 
Ernesto Mordecki
Facultad de Ciencias - Centro de Matematica
Igua 4225 - 11400 - Montevideo - Uruguay
Tel:  (598) 2525 25 22 interno 122.
Fax: (598) 2522 06 53
http://www.cmat.edu.uy/~mordecki/
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