PITT_2008.TEX
SPARSE GRIDS:
Turning High Dimensional Data into Information

I gave a talk on 11 November 2008, to the Computational Mathematics Seminar at the University of Pittsburgh Mathematics Department. The talk was titled

SPARSE GRIDS: Turning High Dimensional Data into Information

A plain text abstract of the talk is available as pitt_2008_abstract.txt.

A PDF version is available as ../../presentations/pitt_2008.pdf.

Some information on the sparse grid research I participated in is included in these references:

1. John Burkardt, Max Gunzburger, Clayton Webster,
   Reduced Order Modeling of Some Nonlinear Stochastic Partial Differential Equations,
   International Journal of Numerical Analysis and Modeling,
   Volume 4, Number 3-4, 2007, pages 368-391,
   bgw_ijnam_2007.pdf.
2. Clayton Webster,
   Sparse Grid Stochastic Collocation Techniques for the Numerical Solution of Partial Differential Equations with Random Input Data,
   PhD Dissertation,
   Mathematics Department,
   Florida State University, May 2007,
   webster_thesis.pdf.

The following files constitute the LaTeX file used to create the slides:

• pitt_2008.tex, the main LaTeX file;
• multimedia.sty, a LaTeX style file;
• icam_logo.pdf, a PDF image of a logo.

The following graphics files were used:

• art_owen.png, a PNG image of Art Owen, a Stanford researcher in the area of high dimensional quadrature.
• cc_d2_o17x17.png, a PNG image of a 2D product grid made from two order 17 Clenshaw Curtis rules.
• cc_d2_o9x5.png, a PNG image of a 2D product grid made from order 9 and order 5 Clenshaw Curtis rules.
• cc_d3_level5.png, a PNG image of a 3D Smolyak sparse grid of level 5, based on Clenshaw Curtis rules.
• cc_sparse_2d.png, a PNG image of a 2D Smolyak sparse grid of level 4.
• level4_o1x17.png, a PNG image of the 1x17 component of a 2D level 4 sparse grid.
• level4_o3x9.png, a PNG image of the 3x9 component of a 2D level 4 sparse grid.
• level4_o5x5.png, a PNG image of the 5x5 component of a 2D level 4 sparse grid.
• level4_o9x3.png, a PNG image of the 17x1 component of a 2D level 4 sparse grid.
• level4_o17x1.png, a PNG image of the 17x1 component of a 2D level 4 sparse grid.
• mc5_p28.png, a PNG image of the results of 5 distinct Monte Carlo approximations to integrand 28.
• mc5_versus_smolyak_p28.png, a PNG image of a comparison of 5 distinct Monte Carlo approximations versus the Smolyak approach on integrand 28.
• mc_versus_smolyak_p28.png, a PNG image of a comparison of a Monte Carlo approximation versus the Smolyak approach on integrand 28.
• monte_carlo_2d.png, a PNG image of a possible arrangement of the first 1000 sample points in a 2D Monte Carlo procedure.
• monte_carlo_p28.png, a PNG image of the results of a Monte Carlo approximation to integrand 28.
• quasi_monte_carlo_2d.png, a PNG image of a possible arrangement of the first 1000 sample points in a 2D Quasi Monte Carlo procedure.
• sergey_smolyak.png, a PNG image of Sergey Smolyak, who devised the Smolyak sparse grid technique.
• smolyak_p28.png, a PNG image of the results of a series of Smolyak approximations to integrand 28.
• stochastic_mc.pdf, a PDF image of the results of 5 Monte Carlo approximations to the stochastic diffusion problem, in 11D, with varying values of the correlation length L.
• stochastic_mc_and_sm.pdf, a PDF image of a comparison of the Smolyak procedure and 5 Monte Carlo approximations to the stochastic diffusion problem, in 11D, with varying values of the correlation length L.
• wizard.png, a PNG image of a software wizard.

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