NEWTON_INTERP_1D
Polynomial Interpolation with Newton Divided Differences

NEWTON_INTERP_1D, a C++ 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 C++ 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 C++ library which determines the combination of Chebyshev polynomials which interpolates a set of data, so that p(x(i)) = y(i).

DIVDIF, a C++ library which uses divided differences to compute the polynomial interpolant to a given set of data.

HERMITE, a C++ library which computes the Hermite interpolant, a polynomial that matches function values and derivatives.

LAGRANGE_INTERP_1D, a C++ 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 C++ library which interpolates a set of data using a piecewise constant interpolant defined by the nearest neighbor criterion.

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

R8LIB, a C++ library which contains many utility routines, using double precision real (R8) arithmetic.

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

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

SPLINE, a C++ library which constructs and evaluates spline interpolants and approximants.

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

VANDERMONDE_INTERP_1D, a C++ 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_interp_1d.cpp, the source code.
• newton_interp_1d.hpp, the include file.

Examples and Tests:

• newton_interp_1d_test.cpp, a sample calling program.
• newton_interp_1d_test.txt, the output file.

The code generates some plots of the data and approximants.

• plot01.png, a plot of the polynomial interpolant for problem p01;
• plot02.png, a plot of the polynomial interpolant for problem p02;
• plot03.png, a plot of the polynomial interpolant for problem p03;
• plot04.png, a plot of the polynomial interpolant for problem p04;
• plot05.png, a plot of the polynomial interpolant for problem p05;
• plot06.png, a plot of the polynomial interpolant for problem p06;
• plot07.png, a plot of the polynomial interpolant for problem p07;
• plot08.png, a plot of the polynomial interpolant for problem p08;

List of Routines:

• NEWTON_COEF_1D computes coefficients of a Newton 1D interpolant.
• NEWTON_VALUE_1D evaluates a Newton 1D interpolant.
• R8VEC_COPY_NEW copies an R8VEC.
• R8VEC_LINSPACE_NEW creates a vector of linearly spaced values.
• R8VEC_MAX returns the value of the maximum element in a R8VEC.
• R8VEC_MIN returns the value of the minimum element in a R8VEC.
• R8VEC_NORM_AFFINE returns the affine L2 norm of an R8VEC.
• R8VEC_PRINT prints an R8VEC.
• R8VEC2_PRINT prints an R8VEC2.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.