# Accession Number:

## ADP013753

# Title:

## Point Shifts in Rational Interpolation with Optimized Denominator

# Descriptive Note:

## Conference paper

# Corporate Author:

## FRIBOURG UNIV (SWITZERLAND)

# Personal Author(s):

# Report Date:

## 2001-07-01

# Pagination or Media Count:

## 8.0

# Abstract:

In previous work we have suggested obtaining rational interpolants of a function f by attaching optimally placed poles to its interpolating polynomials. For a large number of interpolation points these polynomials are well-known to be good approximants only if the nodes tend to cluster near the endpoints of the interval as with Chebyshev or Legendre points. In practice however, one would prefer to have them closer to equidistant. This will in particular be the case when the difficult portion of f lies well within the interior of the interval, or when approximating derivatives of f, as in the solution of differential equations. To address this difficulty, we use here a conformal change of variable to shift the points from the Chebyshev position toward a more equidistant distribution in a way that should maintain the exponential convergence when f is analytic. Numerical examples demonstrate the resulting improvement in the quality of the approximation.

# Descriptors:

# Subject Categories:

- Numerical Mathematics
- Theoretical Mathematics