least_squares_approximant

least_squares_approximant, a MATLAB code which finds a polynomial approximant to data using linear least squares (LLS).

Licensing:

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

Languages:

least_squares_approximant is available in a MATLAB version.

Related Data and Programs:

chebyshev, a MATLAB code which computes the Chebyshev interpolant/approximant to a given function over an interval.

divdif, a MATLAB code which uses divided differences to compute the polynomial interpolant to a given set of data.

hermite_interpolant, a MATLAB code which computes the Hermite interpolant, a polynomial that matches function values and derivatives.

least_squares_approximant_test

rbf_interp_1d, a MATLAB code which defines and evaluates radial basis function (RBF) interpolants to 1D data.

spline, a MATLAB code which constructs and evaluates spline interpolants and approximants.

test_interp, a MATLAB code which defines a number of test problems for interpolation, provided as a set of (x,y) data.

test_interp_fun, a MATLAB code which defines a number of test problems for interpolation, provided as functions (x,f(x)).

vandermonde_interp_1d, a MATLAB code which finds a polynomial interpolant to data by setting up and solving a linear system involving the Vandermonde matrix.

Reference:

1. Kendall Atkinson,
   An Introduction to Numerical Analysis,
   Prentice Hall, 1989,
   ISBN: 0471624896,
   LC: QA297.A94.1989.
2. Philip Davis,
   Interpolation and Approximation,
   Dover, 1975,
   ISBN: 0-486-62495-1,
   LC: QA221.D33
3. David Kahaner, Cleve Moler, Steven Nash,
   Numerical Methods and Software,
   Prentice Hall, 1989,
   ISBN: 0-13-627258-4,
   LC: TA345.K34.

Source Code:

• least_squares_approximant_coef.m, determines the linear least squares polynomial.
• least_squares_approximant_matrix.m, computes the linear least squares approximant matrix.
• poly_value.m, evaluates a polynomial.
• r8mat_transpose_print.m, prints an R8MAT, transposed.
• r8mat_transpose_print_some.m, prints some of an R8MAT, transposed.