barycentric_interp_1d_test

barycentric_interp_1d_test, an Octave code which calls barycentric_interp_1d() to define and evaluate the Lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i). Because a barycentric formulation is used, polynomials of very high degree can safely be used.

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:

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.

Source Code:

• barycentric_interp_1d_test.m, calls all the tests;
• barycentric_interp_1d_test.sh, runs all the tests;
• barycentric_interp_1d_test.txt, the output file.
• lagcheby1_interp_1d_test.m
• lagcheby2_interp_1d_test.m
• lageven_interp_1d_test.m

lagcheby1_interp_1d_test() samples a function at Chebyshev Type 1 points and determines and plots the barycentric Lagrange polynomial interpolant.

• p01_lagcheby1_04.png, a plot of the interpolant to 4 Chebyshev 1 points for problem p01;
• p01_lagcheby1_08.png, a plot of the interpolant to 8 Chebyshev 1 points for problem p01;
• p01_lagcheby1_16.png, a plot of the interpolant to 16 Chebyshev 1 points for problem p01;
• p01_lagcheby1_32.png, a plot of the interpolant to 32 Chebyshev 1 points for problem p01;
• p01_lagcheby1_64.png, a plot of the interpolant to 64 Chebyshev 1 points for problem p01;
• p02_lagcheby1_04.png, a plot of the interpolant to 4 Chebyshev 1 points for problem p02;
• p02_lagcheby1_08.png, a plot of the interpolant to 8 Chebyshev 1 points for problem p02;
• p02_lagcheby1_16.png, a plot of the interpolant to 16 Chebyshev 1 points for problem p02;
• p02_lagcheby1_32.png, a plot of the interpolant to 32 Chebyshev 1 points for problem p02;
• p02_lagcheby1_64.png, a plot of the interpolant to 64 Chebyshev 1 points for problem p02;
• p03_lagcheby1_04.png, a plot of the interpolant to 4 Chebyshev 1 points for problem p03;
• p03_lagcheby1_08.png, a plot of the interpolant to 8 Chebyshev 1 points for problem p03;
• p03_lagcheby1_16.png, a plot of the interpolant to 16 Chebyshev 1 points for problem p03;
• p03_lagcheby1_32.png, a plot of the interpolant to 32 Chebyshev 1 points for problem p03;
• p03_lagcheby1_64.png, a plot of the interpolant to 64 Chebyshev 1 points for problem p03;
• p04_lagcheby1_04.png, a plot of the interpolant to 4 Chebyshev 1 points for problem p04;
• p04_lagcheby1_08.png, a plot of the interpolant to 8 Chebyshev 1 points for problem p04;
• p04_lagcheby1_16.png, a plot of the interpolant to 16 Chebyshev 1 points for problem p04;
• p04_lagcheby1_32.png, a plot of the interpolant to 32 Chebyshev 1 points for problem p04;
• p04_lagcheby1_64.png, a plot of the interpolant to 64 Chebyshev 1 points for problem p04;
• p05_lagcheby1_04.png, a plot of the interpolant to 4 Chebyshev 1 points for problem p05;
• p05_lagcheby1_08.png, a plot of the interpolant to 8 Chebyshev 1 points for problem p05;
• p05_lagcheby1_16.png, a plot of the interpolant to 16 Chebyshev 1 points for problem p05;
• p05_lagcheby1_32.png, a plot of the interpolant to 32 Chebyshev 1 points for problem p05;
• p05_lagcheby1_64.png, a plot of the interpolant to 64 Chebyshev 1 points for problem p05;
• p06_lagcheby1_04.png, a plot of the interpolant to 4 Chebyshev 1 points for problem p06;
• p06_lagcheby1_08.png, a plot of the interpolant to 8 Chebyshev 1 points for problem p06;
• p06_lagcheby1_16.png, a plot of the interpolant to 16 Chebyshev 1 points for problem p06;
• p06_lagcheby1_32.png, a plot of the interpolant to 32 Chebyshev 1 points for problem p06;
• p06_lagcheby1_64.png, a plot of the interpolant to 64 Chebyshev 1 points for problem p06;
• p07_lagcheby1_04.png, a plot of the interpolant to 4 Chebyshev 1 points for problem p07;
• p07_lagcheby1_08.png, a plot of the interpolant to 8 Chebyshev 1 points for problem p07;
• p07_lagcheby1_16.png, a plot of the interpolant to 16 Chebyshev 1 points for problem p07;
• p07_lagcheby1_32.png, a plot of the interpolant to 32 Chebyshev 1 points for problem p07;
• p07_lagcheby1_64.png, a plot of the interpolant to 64 Chebyshev 1 points for problem p07;
• p08_lagcheby1_04.png, a plot of the interpolant to 4 Chebyshev 1 points for problem p08;
• p08_lagcheby1_08.png, a plot of the interpolant to 8 Chebyshev 1 points for problem p08;
• p08_lagcheby1_16.png, a plot of the interpolant to 16 Chebyshev 1 points for problem p08;
• p08_lagcheby1_32.png, a plot of the interpolant to 32 Chebyshev 1 points for problem p08;
• p08_lagcheby1_64.png, a plot of the interpolant to 64 Chebyshev 1 points for problem p08;

lagcheby2_interp_1d_test samples a function at Chebyshev Type 2 points and determines and plots the barycentric Lagrange polynomial interpolant.

• p01_lagcheby2_04.png, a plot of the interpolant to 4 Chebyshev 2 points for problem p01;
• p01_lagcheby2_08.png, a plot of the interpolant to 8 Chebyshev 2 points for problem p01;
• p01_lagcheby2_16.png, a plot of the interpolant to 16 Chebyshev 2 points for problem p01;
• p01_lagcheby2_32.png, a plot of the interpolant to 32 Chebyshev 2 points for problem p01;
• p01_lagcheby2_64.png, a plot of the interpolant to 64 Chebyshev 2 points for problem p01;
• p02_lagcheby2_04.png, a plot of the interpolant to 4 Chebyshev 2 points for problem p02;
• p02_lagcheby2_08.png, a plot of the interpolant to 8 Chebyshev 2 points for problem p02;
• p02_lagcheby2_16.png, a plot of the interpolant to 16 Chebyshev 2 points for problem p02;
• p02_lagcheby2_32.png, a plot of the interpolant to 32 Chebyshev 2 points for problem p02;
• p02_lagcheby2_64.png, a plot of the interpolant to 64 Chebyshev 2 points for problem p02;
• p03_lagcheby2_04.png, a plot of the interpolant to 4 Chebyshev 2 points for problem p03;
• p03_lagcheby2_08.png, a plot of the interpolant to 8 Chebyshev 2 points for problem p03;
• p03_lagcheby2_16.png, a plot of the interpolant to 16 Chebyshev 2 points for problem p03;
• p03_lagcheby2_32.png, a plot of the interpolant to 32 Chebyshev 2 points for problem p03;
• p03_lagcheby2_64.png, a plot of the interpolant to 64 Chebyshev 2 points for problem p03;
• p04_lagcheby2_04.png, a plot of the interpolant to 4 Chebyshev 2 points for problem p04;
• p04_lagcheby2_08.png, a plot of the interpolant to 8 Chebyshev 2 points for problem p04;
• p04_lagcheby2_16.png, a plot of the interpolant to 16 Chebyshev 2 points for problem p04;
• p04_lagcheby2_32.png, a plot of the interpolant to 32 Chebyshev 2 points for problem p04;
• p04_lagcheby2_64.png, a plot of the interpolant to 64 Chebyshev 2 points for problem p04;
• p05_lagcheby2_04.png, a plot of the interpolant to 4 Chebyshev 2 points for problem p05;
• p05_lagcheby2_08.png, a plot of the interpolant to 8 Chebyshev 2 points for problem p05;
• p05_lagcheby2_16.png, a plot of the interpolant to 16 Chebyshev 2 points for problem p05;
• p05_lagcheby2_32.png, a plot of the interpolant to 32 Chebyshev 2 points for problem p05;
• p05_lagcheby2_64.png, a plot of the interpolant to 64 Chebyshev 2 points for problem p05;
• p06_lagcheby2_04.png, a plot of the interpolant to 4 Chebyshev 2 points for problem p06;
• p06_lagcheby2_08.png, a plot of the interpolant to 8 Chebyshev 2 points for problem p06;
• p06_lagcheby2_16.png, a plot of the interpolant to 16 Chebyshev 2 points for problem p06;
• p06_lagcheby2_32.png, a plot of the interpolant to 32 Chebyshev 2 points for problem p06;
• p06_lagcheby2_64.png, a plot of the interpolant to 64 Chebyshev 2 points for problem p06;
• p07_lagcheby2_04.png, a plot of the interpolant to 4 Chebyshev 2 points for problem p07;
• p07_lagcheby2_08.png, a plot of the interpolant to 8 Chebyshev 2 points for problem p07;
• p07_lagcheby2_16.png, a plot of the interpolant to 16 Chebyshev 2 points for problem p07;
• p07_lagcheby2_32.png, a plot of the interpolant to 32 Chebyshev 2 points for problem p07;
• p07_lagcheby2_64.png, a plot of the interpolant to 64 Chebyshev 2 points for problem p07;
• p08_lagcheby2_04.png, a plot of the interpolant to 4 Chebyshev 2 points for problem p08;
• p08_lagcheby2_08.png, a plot of the interpolant to 8 Chebyshev 2 points for problem p08;
• p08_lagcheby2_16.png, a plot of the interpolant to 16 Chebyshev 2 points for problem p08;
• p08_lagcheby2_32.png, a plot of the interpolant to 32 Chebyshev 2 points for problem p08;
• p08_lagcheby2_64.png, a plot of the interpolant to 64 Chebyshev 2 points for problem p08;