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Barycentric rational interpolation with no poles and high rates of approximation

โœ Scribed by Michael S. Floater; Kai Hormann


Publisher
Springer-Verlag
Year
2007
Tongue
English
Weight
355 KB
Volume
107
Category
Article
ISSN
0029-599X

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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, compu

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From (1) it follows that y ( z ) has in zk a zero of order not less than vk . Since y ( z ) is holomorphic in the neighborhood of every point of %'K (including z = a), it follows from Hypothesis 6, that y ( z ) vanishes identically in VK. On the other hand, we have for large IzJ of 5. 1 We say tha