sparse_2008_pitt
sparse_2008_pitt,
"SPARSE GRIDS: Turning High Dimensional Data into Information",
a talk I gave to the
Computational Mathematics Seminar
at the University of Pittsburgh Mathematics Department,
on 11 November 2008.
A plain text abstract of the talk is available as
sparse_2008_pitt.txt.
Some information on the sparse grid research I participated in
is included in these references:
-
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.
-
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 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.
-
fsu_logo.pdf,
a logo.
-
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 PNG 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 PNG 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.
Last revised on 02 February 2024.