Exponentially Converging Linear Rational Interpolation
Abstract
Rational interpolation by a quotient of two n-th degreee polynomials
becomes a linear process if the denominator polynomial is fixed. We suggest
to determine it such that the corresponding Lebesgue constant is minimized.
The resulting interpolation scheme shows somewhat unsatisfactory behavior
for increasing degree. We thus consider limiting the denominator degree.
Numerical results show near exponential convergence even for equidistant
interpolation points.
This is joint work with Jean-Paul Berrut.
