TOMS726
Orthogonal Polynomials and Quadrature Rules
TOMS726
is a FORTRAN90 library which
computes recursion relationships for various families of
orthogonal polynomials, as well as the abscissas and weights of
related quadrature rules;
the library is commonly called ORTHPOL, and is
by Walter Gautschi.
Languages:
TOMS726 is available in
a FORTRAN77 version and
a FORTRAN90 version.
Related Data and Programs:
TOMS655,
a FORTRAN77 library which
computes the weights for interpolatory quadrature rules.
Reference:

William Cody, Kenneth Hillstrom,
Chebyshev Approximations for the Natural Logarithm of the
Gamma Function,
Mathematics of Computation,
Volume 21, Number 98, April 1967, pages 198203.

Walter Gautschi,
On Generating Orthogonal Polynomials,
SIAM Journal on Scientific and Statistical Computing,
Volume 3, Number 3, 1982, pages 289317.

Walter Gautschi,
Algorithm 726:
ORTHPOL  A Package of Routines for Generating Orthogonal
Polynomials and GaussType Quadrature Rules,
ACM Transactions on Mathematical Software,
Volume 20, Number 1, March 1994, pages 2162.
Source Code:
Examples and Tests:
List of Routines:

ALGA_R8 evaluates the logarithm of the gamma function.

CHEB_R8 implements the modified Chebyshev algorithm.

CHRI_R8 implements the Christoffel or generalized Christoffel theorem.

FEJER_R8 generates a Fejer quadrature rule.

GAMMA_R8 evaluates the gamma function for real positive argument.

GAUSS_R8 generates an Npoint Gaussian quadrature formula.

GCHRI_R8 implements the generalized Christoffel theorem.

KERN_R8 generates the kernels in the Gauss quadrature remainder term.

KNUM_R8 integrates certain rational polynomials.

LANCZ_R8 applies Stieltjes's procedure, using the Lanczos method.

LOB_R8 generates a GaussLobatto quadrature rule.

MCCHEB_R8 is a multiplecomponent discretized modified Chebyshev algorithm.

MCDIS_R8 is a multiplecomponent discretization procedure.

NU0HER estimates a starting index for recursion with the Hermite measure.

NU0JAC estimates a starting index for recursion with the Jacobi measure.

NU0LAG estimates a starting index for recursion with the Laguerre measure.

QGP_R8 is a generalpurpose discretization routine.

RADAU_R8 generates a GaussRadau quadrature formula.

RECUR_R8 generates recursion coefficients for orthogonal polynomials.

STI_R8 applies Stieltjes's procedure.

SYMTR_R8 maps T in [1,1] to X in (oo,oo).

TIMESTAMP prints the current YMDHMS date as a time stamp.

TR_R8 maps T in [1,1] to X in [0,oo).
You can go up one level to
the FORTRAN90 source codes.
Last revised on 28 April 2013.