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An Osculatory Extension of Cauchy's Rational Interpolation Formula
Author(s) -
Salzer H. E.
Publication year - 1984
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19840640108
Subject(s) - mathematics , interpolation (computer graphics) , extension (predicate logic) , generalization , cauchy distribution , pure mathematics , linear interpolation , node (physics) , birkhoff interpolation , mathematical analysis , nearest neighbor interpolation , computer science , polynomial , animation , computer graphics (images) , structural engineering , engineering , programming language
An explicit formula for osculatory rational interpolation, in terms of functional values at every node, and any number of consecutive derivatives at one node, is derived from Cauchy's rational interpolation formula by solving the equivalent problem of finding the corresponding confluent limits of a non‐linear generalization of divided differences.