**vandermonde_approx_2d_test**,
a MATLAB program which
calls vandermonde_approx_2d() to find 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.

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

vandermonde_approx_2d, a MATLAB library which finds a polynomial approximant p(x,y) to data z(x,y) of a 2D argument by setting up and solving an overdetermined linear system for the polynomial coefficients involving the vandermonde matrix.

- vandermonde_approx_2d_test.m, calls all the tests;
- vandermonde_approx_2d_test.sh, runs all the tests;
- vandermonde_approx_2d_test.txt, the output file.

- vandermonde_approx_2d_test01.m, approximates a given test problem with a polynomial of given order.

The code generates some plots of the data and approximants.

- p01_data.png, a plot of the piecewise linear interpolant to the data for problem p01;
- p01_poly00.png, a plot of the polynomial interpolant for problem p01, degree 0;
- p01_poly01.png, a plot of the polynomial interpolant for problem p01, degree 1;
- p01_poly02.png, a plot of the polynomial interpolant for problem p01, degree 2;
- p01_poly04.png, a plot of the polynomial interpolant for problem p01, degree 4;
- p01_poly08.png, a plot of the polynomial interpolant for problem p01, degree 8;
- p02_data.png, a plot of the piecewise linear interpolant to the data for problem p02;
- p02_poly00.png, a plot of the polynomial interpolant for problem p02, degree 0;
- p02_poly01.png, a plot of the polynomial interpolant for problem p02, degree 1;
- p02_poly02.png, a plot of the polynomial interpolant for problem p02, degree 2;
- p02_poly04.png, a plot of the polynomial interpolant for problem p02, degree 4;
- p02_poly08.png, a plot of the polynomial interpolant for problem p02, degree 8;
- p03_data.png, a plot of the piecewise linear interpolant to the data for problem p03;
- p03_poly00.png, a plot of the polynomial interpolant for problem p03, degree 0;
- p03_poly01.png, a plot of the polynomial interpolant for problem p03, degree 1;
- p03_poly02.png, a plot of the polynomial interpolant for problem p03, degree 2;
- p03_poly04.png, a plot of the polynomial interpolant for problem p03, degree 4;
- p03_poly08.png, a plot of the polynomial interpolant for problem p03, degree 8;
- p04_data.png, a plot of the piecewise linear interpolant to the data for problem p04;
- p04_poly00.png, a plot of the polynomial interpolant for problem p04, degree 0;
- p04_poly01.png, a plot of the polynomial interpolant for problem p04, degree 1;
- p04_poly02.png, a plot of the polynomial interpolant for problem p04, degree 2;
- p04_poly04.png, a plot of the polynomial interpolant for problem p04, degree 4;
- p04_poly08.png, a plot of the polynomial interpolant for problem p04, degree 8;
- p05_data.png, a plot of the piecewise linear interpolant to the data for problem p05;
- p05_poly00.png, a plot of the polynomial interpolant for problem p05, degree 0;
- p05_poly01.png, a plot of the polynomial interpolant for problem p05, degree 1;
- p05_poly02.png, a plot of the polynomial interpolant for problem p05, degree 2;
- p05_poly04.png, a plot of the polynomial interpolant for problem p05, degree 4;
- p05_poly08.png, a plot of the polynomial interpolant for problem p05, degree 8;
- p06_data.png, a plot of the piecewise linear interpolant to the data for problem p06;
- p06_poly00.png, a plot of the polynomial interpolant for problem p06, degree 0;
- p06_poly01.png, a plot of the polynomial interpolant for problem p06, degree 1;
- p06_poly02.png, a plot of the polynomial interpolant for problem p06, degree 2;
- p06_poly04.png, a plot of the polynomial interpolant for problem p06, degree 4;
- p06_poly08.png, a plot of the polynomial interpolant for problem p06, degree 8;
- p07_data.png, a plot of the piecewise linear interpolant to the data for problem p07;
- p07_poly00.png, a plot of the polynomial interpolant for problem p07, degree 0;
- p07_poly01.png, a plot of the polynomial interpolant for problem p07, degree 1;
- p07_poly02.png, a plot of the polynomial interpolant for problem p07, degree 2;
- p07_poly04.png, a plot of the polynomial interpolant for problem p07, degree 4;
- p07_poly08.png, a plot of the polynomial interpolant for problem p07, degree 8;
- p08_data.png, a plot of the piecewise linear interpolant to the data for problem p08;
- p08_poly00.png, a plot of the polynomial interpolant for problem p08, degree 0;
- p08_poly01.png, a plot of the polynomial interpolant for problem p08, degree 1;
- p08_poly02.png, a plot of the polynomial interpolant for problem p08, degree 2;
- p08_poly04.png, a plot of the polynomial interpolant for problem p08, degree 4;
- p08_poly08.png, a plot of the polynomial interpolant for problem p08, degree 8;
- p09_data.png, a plot of the piecewise linear interpolant to the data for problem p09;
- p09_poly00.png, a plot of the polynomial interpolant for problem p09, degree 0;
- p09_poly01.png, a plot of the polynomial interpolant for problem p09, degree 1;
- p09_poly02.png, a plot of the polynomial interpolant for problem p09, degree 2;
- p09_poly04.png, a plot of the polynomial interpolant for problem p09, degree 4;
- p09_poly08.png, a plot of the polynomial interpolant for problem p09, degree 8;
- p10_data.png, a plot of the piecewise linear interpolant to the data for problem p10;
- p10_poly00.png, a plot of the polynomial interpolant for problem p10, degree 0;
- p10_poly01.png, a plot of the polynomial interpolant for problem p10, degree 1;
- p10_poly02.png, a plot of the polynomial interpolant for problem p10, degree 2;
- p10_poly04.png, a plot of the polynomial interpolant for problem p10, degree 4;
- p10_poly08.png, a plot of the polynomial interpolant for problem p10, degree 8;
- p11_data.png, a plot of the piecewise linear interpolant to the data for problem p11;
- p11_poly00.png, a plot of the polynomial interpolant for problem p11, degree 0;
- p11_poly01.png, a plot of the polynomial interpolant for problem p11, degree 1;
- p11_poly02.png, a plot of the polynomial interpolant for problem p11, degree 2;
- p11_poly04.png, a plot of the polynomial interpolant for problem p11, degree 4;
- p11_poly08.png, a plot of the polynomial interpolant for problem p11, degree 8;
- p12_data.png, a plot of the piecewise linear interpolant to the data for problem p12;
- p12_poly00.png, a plot of the polynomial interpolant for problem p12, degree 0;
- p12_poly01.png, a plot of the polynomial interpolant for problem p12, degree 1;
- p12_poly02.png, a plot of the polynomial interpolant for problem p12, degree 2;
- p12_poly04.png, a plot of the polynomial interpolant for problem p12, degree 4;
- p12_poly08.png, a plot of the polynomial interpolant for problem p12, degree 8;
- p13_data.png, a plot of the piecewise linear interpolant to the data for problem p13;
- p13_poly00.png, a plot of the polynomial interpolant for problem p13, degree 0;
- p13_poly01.png, a plot of the polynomial interpolant for problem p13, degree 1;
- p13_poly02.png, a plot of the polynomial interpolant for problem p13, degree 2;
- p13_poly04.png, a plot of the polynomial interpolant for problem p13, degree 4;
- p13_poly08.png, a plot of the polynomial interpolant for problem p13, degree 8;