LAGRANGE_APPROX_1D
Approximation in 1D using Lagrange Polynomials

LAGRANGE_APROX_1D is a FORTRAN77 library which defines and evaluates a Lagrange polynomial p(x) of degree M which approximates a set of ND data points (x(i),y(i)).

LAGRANGE_APPROX_1D needs access to the QR_SOLVE and R8LIB libraries. The test code also needs access to the TEST_INTERP_1D library.

Licensing:

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

Languages:

LAGRANGE_APPROX_1D is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

LAGRANGE_INTERP_1D, a FORTRAN77 library which defines and evaluates the Lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i).

PWL_APPROX_1D, a FORTRAN77 library which approximates a set of data using a piecewise linear function.

QR_SOLVE, a FORTRAN77 library which computes the least squares solution of a linear system A*x=b.

R8LIB, a FORTRAN77 library which contains many utility routines using double precision real (R8) arithmetic.

SPLINE, a FORTRAN77 library which constructs and evaluates spline interpolants and approximants.

TEST_APPROX, a FORTRAN77 library which defines test problems for approximation, provided as a set of (x,y) data.

TEST_INTERP_1D, a FORTRAN77 library which defines test problems for interpolation of data y(x), depending on a 2D argument.

VANDERMONDE_APPROX_1D, a FORTRAN77 library which finds a polynomial approximant to data of a 1D argument by setting up and solving an overdetermined linear system for the polynomial coefficients, 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:

• lagrange_approx_1d.f, the source code.
• lagrange_approx_1d.sh, BASH commands to compile the source code.

Examples and Tests:

• lagrange_approx_1d_prb.f, a sample calling program.
• lagrange_approx_1d_prb.sh, BASH commands to compile and run the sample program.
• lagrange_approx_1d_prb_output.txt, the output file.

List of Routines:

• LAGRANGE_APPROX_1D evaluates the Lagrange approximant of degree M.
• LAGRANGE_BASIS_1D evaluates the Lagrange basis polynomials.

You can go up one level to the FORTRAN77 source codes.