A newton's method for best uniform polynomial approximation
I Georgieva, C Hofreither - International Conference on Large-Scale …, 2021 - Springer
International Conference on Large-Scale Scientific Computing, 2021•Springer
We present a novel algorithm, inspired by the recent BRASIL algorithm for rational
approximation, for best uniform polynomial approximation based on a formulation of the
problem as a nonlinear system of equations and barycentric interpolation. We use results on
derivatives of interpolating polynomials with respect to interpolation nodes to compute the
Jacobian matrix. The resulting method is fast and stable, can deal with singularities and
exhibits superlinear convergence in a neighborhood of the solution.
approximation, for best uniform polynomial approximation based on a formulation of the
problem as a nonlinear system of equations and barycentric interpolation. We use results on
derivatives of interpolating polynomials with respect to interpolation nodes to compute the
Jacobian matrix. The resulting method is fast and stable, can deal with singularities and
exhibits superlinear convergence in a neighborhood of the solution.
Abstract
We present a novel algorithm, inspired by the recent BRASIL algorithm for rational approximation, for best uniform polynomial approximation based on a formulation of the problem as a nonlinear system of equations and barycentric interpolation. We use results on derivatives of interpolating polynomials with respect to interpolation nodes to compute the Jacobian matrix. The resulting method is fast and stable, can deal with singularities and exhibits superlinear convergence in a neighborhood of the solution.
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