newton_interp_1d

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

NEWTON_INTERP_1D needs access to the R8LIB libraries. The test code also needs access to the TEST_INTERP code.

Licensing:

The computer code and data files described and made available on this web page are 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 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_1d, a python code which defines test problems for interpolation of data y(x), depending on a 2d 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:

• newton_interp_1d.py, the source code.
• newton_interp_1d.sh, runs all the tests;
• newton_interp_1d.txt, the output file.

The code generates some plots of the data and approximants.

• p01_data.png, a plot of the data and piecewise linear interpolant for problem p01;
• p01_newton.png, a plot of the polynomial interpolant for problem p01;
• p02_data.png, a plot of the data and piecewise linear interpolant for problem p02;
• p02_newton.png, a plot of the polynomial interpolant for problem p02;
• p03_data.png, a plot of the data and piecewise linear interpolant for problem p03;
• p03_newton.png, a plot of the polynomial interpolant for problem p03;
• p04_data.png, a plot of the data and piecewise linear interpolant for problem p04;
• p04_newton.png, a plot of the polynomial interpolant for problem p04;
• p05_data.png, a plot of the data and piecewise linear interpolant for problem p05;
• p05_newton.png, a plot of the polynomial interpolant for problem p05;
• p06_data.png, a plot of the data and piecewise linear interpolant for problem p06;
• p06_newton.png, a plot of the polynomial interpolant for problem p06;
• p07_data.png, a plot of the data and piecewise linear interpolant for problem p07;
• p07_newton.png, a plot of the polynomial interpolant for problem p07;
• p08_data.png, a plot of the data and piecewise linear interpolant for problem p08;
• p08_newton.png, a plot of the polynomial interpolant for problem p08;