Sparse Pseudospectral Approximation Method

Mathematics – Numerical Analysis

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Scientific paper

Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses a numerical integration rule to approximate the Fourier-type coefficients of a truncated expansion in orthogonal polynomials. For problems in more than two or three dimensions, a sparse grid numerical integration rule offers accuracy with a smaller node set compared to tensor product approximation. However, when using a sparse rule to approximately integrate these coefficients, one often finds unacceptable errors in the coefficients associated with higher degree polynomials. By reexamining Smolyak's algorithm and exploiting the connections between interpolation and projection in tensor product spaces, we construct a sparse pseudospectral approximation method that accurately reproduces the coefficients of basis functions that naturally correspond to the sparse grid integration rule. The compelling numerical results show that this is the proper way to use sparse grid integration rules for pseudospectral approximation.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Sparse Pseudospectral Approximation Method does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sparse Pseudospectral Approximation Method, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sparse Pseudospectral Approximation Method will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-568431

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.