Approximation by rational functions

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:

• rational functions
• interpolation problem
• neighbouring interpolants

Acknowledgement

This work was partially supported by RFBR (Grant 05-01-00250).