lebesgue_test

lebesgue_test, a MATLAB program which calls lebesgue() to plot the Lebesgue function, and estimate the Lebesgue constant, which measures the maximum magnitude of the potential error of Lagrange polynomial interpolation.

Licensing:

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

Related Data and Programs:

lebesgue, a MATLAB library which is given a set of nodes in 1D, and plots the Lebesgue function, and estimates the Lebesgue constant, which measures the maximum magnitude of the potential error of Lagrange polynomial interpolation.

Source Code:

• lebesgue_test.m, calls all the tests;
• lebesgue_test.sh, runs all the tests;
• lebesgue_test.txt, the output file.

• lebesgue_chebyshev1_test.m, examines point sets computed by chebyshev1().
• lebesgue_chebyshev2_test.m, examines point sets computed by chebyshev2().
• lebesgue_chebyshev3_test.m, examines point sets computed by chebyshev3().
• lebesgue_chebyshev4_test.m, examines point sets computed by chebyshev4().
• lebesgue_equidistant1_test.m, examines point sets computed by equidistant1().
• lebesgue_equidistant2_test.m, examines point sets computed by equidistant2().
• lebesgue_equidistant3_test.m, examines point sets computed by equidistant3().
• lebesgue_test08.m, examines point sets computed by fejer1().
• lebesgue_test09.m, examines point sets computed by fejer2().

The test programs create plots of the Lebesgue function for specific sizes of the point sets.

• chebyshev1.png
• chebyshev2.png
• chebyshev3.png
• chebyshev4.png
• equidistant1.png
• equidistant2.png
• equidistant3.png
• fejer1.png
• fejer2.png