unit1

AM205 Unit 1: Data Fitting

vander_cond.py

Constructs the Vandermonde matrix on equidistant points. Measures the growth rate of the condition number depending on the number of points.

vander_interp.py

Performs interpolation using equidistant points by solving a linear system with the Vandermonde matrix.

cheb_interp.py

Performs interpolation using Chebyshev points in the Lagrange polynomial basis.

lebesgue_const.py

Plots the sum of Lagrange polynomials and computes the Lebesgue constant for equidistant or Chebyshev points.

spline_tdma.py

Constructs a cubic spline with clamped boundary conditions by solving a tridiagonal system using the TDMA algorithm.

lstsq.py

Performs linear least-squares fitting in the monomial basis using either the function numpy.linals.lstsq or by solving the normal equations.

nonpoly_fit.py

Performs linear least-squares fitting in the basis of exponentials.

under_lstsq.py

Solves an underdetermined least-squares problem using either the function numpy.linals.lstsq or by solving the normal equations with a regularizer.

nonlin_lstsq.py

Solves the problem of locating a transmitter given distances to beacons using the Levenberg-Marquardt algorithm from scipy.optimize.root.