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Approximation by rational functions

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Abstract:

The inverse problem of finding point sources from finite measurements of two-dimensional stationary field leads to the problem of interpolation by rational functions. However, unlike the polynomial interpolation, the system of equations for the polynomial coefficients appearing here is rather difficult to analyse and to solve numerically. The author has developed a new approach to the investigation of this classical problem, based on the polynomial algebra avoiding systems of linear equations. Rational interpolants are constructed explicitly.

Keywords: interpolation problem; neighbouring interpolants; rational functions

Document Type: Research Article

DOI: https://doi.org/10.1080/00036810802079277

Affiliations: Siberian University of Consumer's Co-Operation, Novosibirsk, Russia

Publication date: 2008-10-01

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