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The barycentric weights of rational interpolation with prescribed poles

✍ Scribed by Jean-Paul Berrut

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
401 KB
Volume
86
Category
Article
ISSN
0377-0427

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✦ Synopsis

We introduce a method for calculating rational interpolants when some (but not necessarily all) of their poles are prescribed. The algorithm determines the weights in the barycentric representation of the rationals; it simply consists in multiplying each interpolated value by a certain number, computing the weights of a rational interpolant without poles, and finally multiplying the weights by those same numbers. The supplementary cost in comparison with interpolation without poles is about (v + 2)N, where v is the number of poles and N the number of interpolation points. We also give a condition under which the computed rational interpolation really shows the desired poles.

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Let x0 .... ,XN be N + 1 interpolation points (nodes) and f0,...,fN be N+ 1 interpolation data. Then every rational function r with numerator and denominator degrees ~<N interpolating these values can be written in its barycentric form ## r(x) = x-x---SJkl x-xk, which is completely determined by