lagrange_interp_1d, an Octave code which defines and evaluates the Lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i).
The test uses the test_interp_1d() library.
The computer code and data files described and made available on this web page are distributed under the MIT license
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.
barycentric_interp_1d, an Octave 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, an Octave code which determines the combination of Chebyshev polynomials which interpolates a set of data, so that p(x(i)) = y(i).
divdif, an Octave code which uses divided differences to compute the polynomial interpolant to a given set of data.
fem1d_lagrange, an Octave code 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_interpolant, an Octave code which computes the Hermite interpolant, a polynomial that matches function values and derivatives.
lagrange_approx_1d, an Octave code 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, an Octave code which displays the basis functions associated with a given set of nodes used with the Lagrange interpolation scheme.
lagrange_interp_2d, an Octave code 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, an Octave code 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, an Octave code which interpolates a set of data using a piecewise constant interpolant defined by the nearest neighbor criterion.
newton_interp_1d, an Octave code which finds a polynomial interpolant to data using Newton divided differences.
pwl_interp_1d, an Octave code which interpolates a set of data using a piecewise linear (PWL) interpolant.
rbf_interp_1d, an Octave code which defines and evaluates radial basis function (RBF) interpolants to 1d data.
shepard_interp_1d, an Octave code which defines and evaluates Shepard interpolants to 1d data, which are based on inverse distance weighting.
spline, an Octave code which constructs and evaluates spline interpolants and approximants.
test_interp_1d, an Octave code which defines test problems for interpolation of data y(x), depending on a 1d argument.
vandermonde_interp_1d, an Octave code which finds a polynomial interpolant to a function of 1d data by setting up and solving a linear system for the polynomial coefficients, involving the Vandermonde matrix.