line_fekete_rule, an Octave code which approximates the location of Fekete points in an interval [A,B]. A family of sets of Fekete points, indexed by size N, represents an excellent choice for defining a polynomial interpolant.
Given a desired number of points N, the best choice for abscissas is a set of Lebesgue points, which minimize the Lebesgue constant, which describes the error in polynomial interpolation. Sets of Lebesgue points are difficult to define mathematically. Fekete points are a related, computable set, defined as those sets maximizing the magnitude of the determinant of the Vandermonde matrix associated with the points. Analytic definitions of these points are known for a few cases, but there is a general computational procedure for approximating them, which is demonstrated here.
The computer code and data files described and made available on this web page are distributed under the MIT license
line_fekete_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and a Octave version.
line_felippa_rule, an Octave code which returns the points and weights of a felippa quadrature rule over the interior of a line segment in 1d.