[SciPy-Dev] Introduction and feature proposal.

[Christopher Miller]

Hello,

My name is Chris Miller and I'm a recent applied math PhD from 
University of Maryland. I have some matlab and C/C++ code for computing 
multi-dimensional integrals using Smolyak sparse grids that I think 
might fit well inside scipy.integrate. Sparse grid quadrature delays the 
onset of the so called "curse of dimensionality," and is very efficient 
for evaluating integrals with a 'moderate' number of variables, say 
~<50. Sparse grids rules can also be tailored to perform integration 
with respect to various measures (uniform, Gaussian, beta-distribution, 
etc.). I'd appreciate any feedback on whether or not people would find 
this useful.

I also have a pretty good background in sparse numerical linear algebra 
and multigrid preconditioners, and would like to contribute code in that 
vein some time down the road. I'm looking forward to working with all of 
you and hope I can be helpful.

Chris

p.s. Here are some references. Most of my work with these was in solving 
stochastic PDEs, so the references tilt that way, but they are generally 
useful tools for multi-dimensional integration/interpolation.

D. Xiu and J. Hesthaven. High-order collocation methods for differential 
equa-
tions with random inputs. SIAM Journal on Scientific Computing, 27:1118–
1139, 2005.

F. Nobile, R. Tempone, and C.G. Webster. An anisotropic sparse grid col-
location algorithm for the solution of stochastic differential 
equations. SIAM
Journal on Numerical Analysis, 46:2411–2442, 2008.