lagrange_interp_1d


lagrange_interp_1d, a FORTRAN77 code which defines and evaluates the Lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i).

The code needs the R8LIB() library. The test uses the TEST_INTERP_1D library.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

lagrange_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:

lagrange_interp_1d_test

barycentric_interp_1d, a FORTRAN77 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 FORTRAN77 library which determines the combination of Chebyshev polynomials which interpolates a set of data, so that p(x(i)) = y(i).

DIVDIF, a FORTRAN77 library which uses divided differences to compute the polynomial interpolant to a given set of data.

FEM1D_LAGRANGE, a FORTRAN77 library which sets up the matrices and vectors associated with the finite element method (FEM) solution of a boundary value problem (BVP) -u''+u=f(x), using Lagrange basis polynomials.

HERMITE, a FORTRAN77 library which computes the Hermite interpolant, a polynomial that matches function values and derivatives.

LAGRANGE_APPROX_1D, a FORTRAN77 library which defines and evaluates the Lagrange polynomial p(x) of degree m which approximates a set of nd data points (x(i),y(i)).

LAGRANGE_BASIS_DISPLAY, a MATLAB library which displays the basis functions associated with a given set of nodes used with the Lagrange interpolation scheme.

LAGRANGE_INTERP_2D, a FORTRAN77 library which defines and evaluates the Lagrange polynomial p(x,y) which interpolates a set of data depending on a 2D argument that was evaluated on a product grid, so that p(x(i),y(j)) = z(i,j).

LAGRANGE_INTERP_ND, a FORTRAN77 library which defines and evaluates the Lagrange polynomial p(x) which interpolates a set of data depending on a multidimensional argument x that was evaluated on a product grid, so that p(x(i)) = z(i).

NEAREST_INTERP_1D, a FORTRAN77 library which interpolates a set of data using a piecewise constant interpolant defined by the nearest neighbor criterion.

PWL_INTERP_1D, a FORTRAN77 library which interpolates a set of data using a piecewise linear interpolant.

R8LIB, a FORTRAN77 library which contains many utility routines using double precision real (R8) arithmetic.

RBF_INTERP_1D, a FORTRAN77 library which defines and evaluates radial basis function (RBF) interpolants to 1D data.

SHEPARD_INTERP_1D, a FORTRAN77 library which defines and evaluates Shepard interpolants to 1D data, based on inverse distance weighting.

SPLINE, a FORTRAN77 library which constructs and evaluates spline interpolants and approximants.

TEST_INTERP, a FORTRAN77 library which defines a number of test problems for interpolation, provided as a set of (x,y) data.

TEST_INTERP_1D, a FORTRAN77 library which defines test problems for interpolation of data y(x), depending on a 2D argument.

VANDERMONDE_INTERP_1D, a FORTRAN77 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:


Last revised on 18 October 2023.