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Erschienen in:
2005 | OriginalPaper | Buchkapitel
(0, 2) Pál-type Interpolation: A General Method for Regularity
verfasst von : Marcel G. de Bruin, Detlef H. Mache
Erschienen in: Trends and Applications in Constructive Approximation
Verlag: Birkhäuser Basel
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The methods of proof of regularity for interpolation problems often are dependent on the problem at hand. In case of given pairs of node generating polynomials the method of deriving an ordinary differential equation for the interpolating polynomial or that of exploiting the specific form of the node generator have mainly been used up to now.
Recently another method was used in the case of Pál-type interpolation where ‘only’ one of the node generators is fixed in advance: a ‘general’ method of deriving a companion generator that leads to a regular interpolation problem. Using (0, 2) Pál-type interpolation, it is shown that each of the methods has its merits and for sake of simplicity we will restrict ourselves to the case that the nodes are the zeros of pairs of polynomials of the following form: {
p
(
z
)
q
(
z
),
p
(
z
)} with
p, q
co-prime and both having simple zeros.