vandermonde_approx_1d, an Octave code which finds a polynomial approximant to 1D data by setting up and solving an overdetermined linear system involving the Vandermonde matrix.
This software is primarily intended as an illustration of the problems that can occur when the approximation problem is naively formulated using the Vandermonde matrix. Unless the data points are well separated, and the degree of the polynomial is low, the linear system will become very difficult to store and solve accurately, because the monomials used as basis vectors by the Vandermonde approach become indistinguishable.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
vandermonde_approx_1d is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and a Python version.
bernstein_polynomial, an Octave code which evaluates the Bernstein polynomials, useful for uniform approximation of functions;
chebyshev, an Octave code which computes the Chebyshev interpolant/approximant to a given function over an interval.
vandermonde_interp_1d, an Octave code which finds a polynomial interpolant to a function of 1D data by setting up and solving a linear system for the polynomial coefficients, involving the Vandermonde matrix.
The code generates some plots of the data and approximants.