vandermonde_approx_2d_test

vandermonde_approx_2d_test, an Octave code which calls vandermonde_approx_2d(), 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.

Licensing:

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

Related Data and Programs:

vandermonde_approx_2d, an Octave code 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.

Source Code:

• 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;