Numerical Integration

Robert M. Corless and Nicolas Fillion
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Robert M. Corless: University of Western Ontario, Applied Mathematics
Nicolas Fillion: University of Western Ontario, Applied Mathematics

Chapter Chapter 10 in A Graduate Introduction to Numerical Methods, 2013, pp 419-462 from Springer

Abstract: Abstract We show that in an absolute sense, integration is well-conditioned but that in a relative sense, integration can be ill-conditioned. We interpret standard algorithms as finding the exact integrals of nearby functions. We discuss several methods, including adaptive methods, Gaussian quadrature, and methods for oscillatory integrands. We pay some attention to the issue of singularity. ⊲

Keywords: Chebyshev Polynomial; Trapezoidal Rule; Quadrature Rule; Gaussian Quadrature; Hermite Interpolation (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-8453-0_10

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DOI: 10.1007/978-1-4614-8453-0_10

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