I shall talk about how to design fast spectral-Galerkin algorithms forsome prototypical partial differential equations. We shall start withalgorithms in one dimension, then using a tensor product approach fortwo and three dimensions, and hyperbolic cross/spectral sparse gridfor higher dimensional problems.
Creator:
Shen, Jie (Purdue University)
Created:
2010-10-31
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Many scientific, engineering and financial applications requiresolving high-dimensional PDEs. However, traditional tensor productbased algorithms suffer from the so called 'curse of dimensionality'.We shall construct a new sparse spectral method forhigh-dimensional problems, and present, in particular,rigorous error estimates as well as efficien...
Creator:
Shen, Jie (Purdue University)
Created:
2010-11-03
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Identification of rare variants by resequencing is important both for detecting novel variations and for screening individuals for known disease alleles. New technologies enable low-cost resequencing of target regions, although it is still prohibitive to test more than a few individuals. We propose a novel pooling design that enables the recover...
Creator:
Shental, Noam (Open University of Israel)
Created:
2012-02-13
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.