newton_interp_1d


newton_interp_1d, a Python code which finds a polynomial interpolant to data using Newton divided differences.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

newton_interp_1d is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

barycentric_interp_1d, a Python code which defines and evaluates the barycentric Lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i). The barycentric approach means that very high degree polynomials can safely be used.

chebyshev_interp_1d, a Python code which determines the combination of Chebyshev polynomials which interpolates a set of data, so that p(x(i)) = y(i).

lagrange_interp_1d, a Python code which defines and evaluates the Lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i).

nearest_interp_1d, a Python code which interpolates a set of data using a piecewise constant interpolant defined by the nearest neighbor criterion.

pwl_interp_1d, a Python code which interpolates a set of data using a piecewise linear interpolant.

rbf_interp_1d, a Python code which defines and evaluates radial basis function (RBF) interpolants to 1d data.

shepard_interp_1d, a Python code which defines and evaluates Shepard interpolants to 1D data, which are based on inverse distance weighting.

test_interp, a Python code which defines test problems for interpolation of data y(x), depending on a 1D argument.

vandermonde_interp_1d, a Python code which finds a polynomial interpolant to data y(x) of a 1D argument by setting up and solving a linear system for the polynomial coefficients, involving the Vandermonde matrix.

Reference:

  1. Kendall Atkinson,
    An Introduction to Numerical Analysis,
    Prentice Hall, 1989,
    ISBN: 0471624896,
    LC: QA297.A94.1989.
  2. Philip Davis,
    Interpolation and Approximation,
    Dover, 1975,
    ISBN: 0-486-62495-1,
    LC: QA221.D33
  3. David Kahaner, Cleve Moler, Steven Nash,
    Numerical Methods and Software,
    Prentice Hall, 1989,
    ISBN: 0-13-627258-4,
    LC: TA345.K34.

Source Code:

The code generates some plots of the data and approximants.


Last modified on 28 January 2020.