lagrange_approx_1d


lagrange_approx_1d, an Octave code which defines and evaluates a Lagrange polynomial p(x) of degree M which approximates a set of ND data points (x(i),y(i)).

LAGRANGE_APPROX_1D needs access to the R8LIB library. The test code also needs access to the TEST_INTERP_1D library.

Licensing:

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

Languages:

lagrange_approx_1d is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:

lagrange_approx_1d_test

bernstein_polynomial, an Octave code which evaluates the Bernstein polynomials, useful for uniform approximation of functions;

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_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).

pwl_approx_1d, an Octave code which approximates a set of data using a piecewise linear function.

r8lib, an Octave code which contains many utility routines using double precision real (R8) arithmetic.

spline, an Octave code which constructs and evaluates spline interpolants and approximants.

test_approx, an Octave code which defines test problems for approximation, provided as a set of (x,y) data.

test_interp_1d, an Octave code which defines test problems for interpolation of data y(x), depending on a 2D argument.

vandermonde_approx_1d, an Octave code which finds a polynomial approximant to data of a 1D argument by setting up and solving an overdetermined 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 06 February 2019.