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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Masterclass: singular integrals and orthogonal polynomials
Masterclass: singular integrals and orthogonal polynomialsAdd to your list(s) Download to your calendar using vCal
If you have a question about this talk, please contact INI IT. This talk has been canceled/deleted Orthogonal polynomials are fundamental tools in numerical methods, including for numerical methods for singular integral equations. A known result is that Cauchy transforms of weighted orthogonal polynomials satisfy the same three-term recurrences as the orthogonal polynomials themselves for n > 0. This basic fact leads to extremely effective schemes of calculating singular integrals that converge spectrally fast (faster than any algebraic power), uniformly in the complex plane. Closed formulae for Cauchy transforms on more complicated geometries are derivable using the Plemelj lemma. These techniques extend to other singular integrals such as those with logarithmic kernels. This talk is part of the Isaac Newton Institute Seminar Series series. This talk is included in these lists:This talk is not included in any other list Note that ex-directory lists are not shown. |
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