polynomial_legendre

polynomial_legendre, introduces the Legendre family of orthogonal polynomials and their uses.

The notes:

Scripts:

bumpy.m, an oscillatory function to interpolate or approximate.
hump.m, a difficult function to interpolate or approximate.
legendre_approximate.m, uses the Legendre basis to approximate a function.
legendre_approximate_humps.m
legendre_approximate_sin.m
legendre_coefficients.m, returns coefficients of the Legendre polynomial P(d,x).
legendre_combo_norm.m, computes the L2 norm of a linear combination of Legendre polynomials, and compares it to the weighted sum of the squares of coefficients.
legendre_combo_value.m, evaluates a linear combination of Legendre polynomials.
legendre_dot_product_test.m, dot product and angle of the i and j Legendre polynomials
legendre_interpolant_bumpy.m, uses Legendre polynomials to interpolate bumpy(x).
legendre_plot.m, plots Legendre polynomials.
legendre_value.m, evaluates a Legendre polynomial.
legendre_value_ab.m, evaluates a Legendre polynomial defined for the interval [a,b].
monomial_approximate.m, c=monomial_approximate(f,d) uses the monomial basis to compute the coefficients of a polynomial that is the least squares approximant to f(x) in [-1,+1].
monomial_approximate_humps.m
monomial_approximate_sin.m
monomial_dot_product_test.m, dot product and angle of the i and j monomials.
monomial_interpolant_bumpy.m, uses monomials to interpolate bumpy(x).
monomial_plot.m, plots some monomials.
poly_value_nested.m, uses nested multiplication to evaluate a polynomial.
runge.m

Text:

legendre_coefficients_pseudocode.txt, pseudocode to determine coefficients of the Legendre polynomial P(d,x).
legendre_value_pseudocode.txt, _pseudocode to evaluate a Legendre polynomial at x.

Images:

Last revised on 11 November 2019.