VANDERMONDE_APPROX_2D
Data Approximation with Polynomials using the Vandermonde Matrix


VANDERMONDE_APPROX_2D, a MATLAB library which finds P(X,Y), a polynomial approximant to Z which depends on two independent variables X and Y, by setting up and solving an overdetermined linear system involving the Vandermonde matrix.

This software is primarily intended as an illustration of the problems that can occur when the approximation problem is naively formulated using the Vandermonde matrix. Unless the data points are well separated, and the degree of the polynomial is low, the linear system will become very difficult to store and solve accurately, because the monomials used as basis vectors by the Vandermonde approach become indistinguishable.

VANDERMONDE_APPROX_2D needs access to the QR_SOLVE and R8LIB libraries. The test code also needs access to the TEST_INTERP_2D library.

Licensing:

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

Languages:

VANDERMONDE_APPROX_2D is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

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

TEST_INTERP_2D, a MATLAB library which defines test problems for interpolation of data (x,y,z(x,y)), with the data points (x,y) scattered irregularly.

VANDERMONDE_APPROX_1D, a MATLAB library which finds a polynomial approximant to data y(x) of a 1D argument by setting up and solving an overdetermined linear system for the polynomial coefficients, involving the Vandermonde matrix.

vandermonde_approx_2d_test

VANDERMONDE_INTERP_2D, a MATLAB library which finds a polynomial interpolant to data z(x,y) of a 2D 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 modified on 22 February 2019.