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Unattainable Points in Multivariate Rational Interpolation

✍ Scribed by H. Allouche; A. Cuyt

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
423 KB
Volume
72
Category
Article
ISSN
0021-9045

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✦ Synopsis

The problem of unattainable points is typical for the case of rational interpolation. Having computed the rational interpolant (p / q) from "linearized" interpolation conditions, in other words, conditions expressed for (f q-p) instead of for (f-(p / q)), it may occur that an interpolation point is also a common zero of (p) and (q) and hence that the rational function (p / q) is undefined in that interpolation point. Consequently the "nonlinear" interpolation condition cannot be satisfied in that interpolation point anymore, not even by the irreducible form of (p / q). The interpolation point has become "unattainable." 1993 Academic Press, Inc.

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