interpolation_lagrange

interpolation_lagrange, looks at how Lagrange basis functions can be used to create a polynomial interpolant to data.

The notes:

• interpolation_lagrange.pdf
• interpolation_lagrange.tex

Scripts:

• basis_lagrange.m, over the interval [a,b], plot n Lagrange basis functions for equally spaced data.
• ell.m, evaluates the j-th Lagrange basis function.
• exp_any.m, interpolation of any order to exp(x). User supplies the value of n as input.
• exp_linear.m, linear interpolation to exp(x).
• exp_quadratic.m, quadratic interpolation of exp(x).
• humps_lagrange.m, interpolation of any order to humps(x). User supplies the value of n as input.
• omega.m, evaluate the omega function.
• omega_plot.m, plot the omega function.

Images:

• basis_lagrange.png, a plot of Lagrange basis functions.
• exp_any.png, interpolation of exp(x) using n=4.
• exp_linear.png, a plot of a linear interpolant to exp(x).
• exp_quadratic.png, a plot of quadratic interpolation of exp(x).
• fingers.png
• humps_lagrange.png, a plot of the humps(x) function using n = 17.
• omega_plot.png, plots of the omega function over [0,3.5] using 1, 3, 5, 9, 17, 33 equally spaced points.