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Extensions of Gauss Quadrature Via Linear Programming
Cited 39 time in
Web of Science
Cited 45 time in Scopus
- Authors
- Issue Date
- 2015-08
- Publisher
- Springer Verlag
- Citation
- Foundations of Computational Mathematics, Vol.15 No.4, pp.953-971
- Abstract
- Gauss quadrature is a well-known method for estimating the integral of a continuous function with respect to a given measure as a weighted sum of the function evaluated at a set of node points. Gauss quadrature is traditionally developed using orthogonal polynomials. We show that Gauss quadrature can also be obtained as the solution to an infinite-dimensional linear program (LP): minimize the th moment among all nonnegative measures that match the through moments of the given measure. While this infinite-dimensional LP provides no computational advantage in the traditional setting of integration on the real line, it can be used to construct Gauss-like quadratures in more general settings, including arbitrary domains in multiple dimensions.
- ISSN
- 1615-3375
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