line_fekete_rule, a Fortran77 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.
[ nf, xf, wf, vf ] = line_fekete_monomial ( n, a, b, m, x )where the input is:
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line_fekete_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.
f77_rule, a Fortran77 code which computes a quadrature rule which estimates the integral of a function f(x), which might be defined over a one dimensional region (a line) or more complex shapes such as a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional region, and which might include an associated weight function w(x).