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
Barycentric rational interpolation with no poles and high rates of approximation
โ 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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๐ SIMILAR VOLUMES
Rational interpolants with prescribed poles are used to approximate holomorphic functions on the closure of their region of analyticity under natural assumptions of their properties on the boundary. The transfer functions of some infinite dimensional dynamical systems of interest in applications sat
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