NEWTON_INTERP_1D
Polynomial Interpolation with Newton Divided Differences

NEWTON_INTERP_1D is a Python library 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 library.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL 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 library 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 library 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 library 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 library which interpolates a set of data using a piecewise constant interpolant defined by the nearest neighbor criterion.

PWL_INTERP_1D, a Python library which interpolates a set of data using a piecewise linear interpolant.

RBF_INTERP_1D, a Python library which defines and evaluates radial basis function (RBF) interpolants to 1D data.

SHEPARD_INTERP_1D, a Python library which defines and evaluates Shepard interpolants to 1D data, which are based on inverse distance weighting.

TEST_INTERP_1D, a Python library which defines test problems for interpolation of data y(x), depending on a 2D argument.

VANDERMONDE_INTERP_1D, a Python library 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_coef_1d.py, solves the Vandermonde system of equations for the coefficients of the polynomial that interpolates a given set of (x,y) data.
• newton_value_1d.py, evaluates a Vandermonde interpolant.
• p00_data.py, returns the data for any problem.
• p00_data_num.py, returns the number of data points for any problem.
• p00_dim_num.py, returns the spatial dimension for any problem.
• p00_prob_num.py, returns the number of test problems.
• r8mat_transpose_print.py, prints an R8MAT, transposed.
• r8mat_transpose_print_some.py, prints some of an R8MAT, transposed.
• r8vec_norm.py, computes the L2 norm of an R8VEC.
• r8vec_norm_affine.py, computes the L2 norm of the difference of two R8VEC's.
• r8vec_print.py, prints an R8VEC.
• r8vec_uniform_ab.py, returns a scaled pseudorandom R8VEC.
• r8vec2_print.py, prints a pair of R8VEC's.
• timestamp.py, prints the YMDHMS date as a timestamp.

Examples and Tests:

• newton_interp_1d_test.py, calls all the tests;
• newton_interp_1d_test.sh, runs all the tests;
• newton_interp_1d_test.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;

You can go up one level to the Python source codes.