CC_PROJECT
ClenshawCurtisLike Quadrature for SemiInfinite and Infinite Intervals
CC_PROJECT
is a MATLAB library which
investigates the extension of a ClenshawCurtislike quadrature
scheme to semiinfinite and infinite intervals, and to integrands
with a specified density function.
The Legendre integral for f(x) is:
I(f) = integral ( 1 <= x <= +1 ) f(x) dx
Quadrature rules for the Legendre integral include:

ClenshawCurtis quadrature, a sequence of nested quadrature rules,
which include the endpoints; the rule of order N has exactness
N1 (if N is even) or N (if N is odd);

Fejer Type 2 quadrature, a sequence of nested quadrature rules,
which include the endpoints; the rule of order N has exactness
N1 (if N is even) or N (if N is odd);
The Laguerre integral for f(x) is:
I(f) = integral ( 0 <= x <= +oo ) f(x) rho(x) dx
Depending on the value of the density function rho(x) we have:

rho(x) = exp(x): Laguerre 0 integral;

rho(x) = 1: Laguerre 1 integral.
Quadrature rules include:

CCFI_0 rules for integral ( 0 <= x <= +oo ) f(x) exp(x) dx;

CCFI_1 rules for integral ( 0 <= x <= +oo ) f(x) dx.
Licensing:
The computer code and data files made available on this web page
are distributed under
the GNU LGPL license.
Languages:
CC_PROJECT is available in
a MATLAB version.
Related Data and Programs:
Reference:

John Boyd,
Exponentially convergent FourierChebyshev quadrature schemes on
bounded and infinite intervals,
Journal of Scientific Computing,
Volume 2, Number 2, 1987, pages 99109.
Source Code:

cardinal_cos.m,
evaluates a cardinal cosine interpolation basis function.

cardinal_sin.m,
evaluates a cardinal sine interpolation basis function.

ccff.m,
defines points and weights for Boyd's quadrature rule
for [1,1] with density 1.

ccff_asymptotic.m,
examines asymptotic error for a given integrand,
for Boyd's quadrature rule for [1,+1]
with density 1.

ccfi_0.m,
defines points and weights for Boyd's quadrature rule
for [0,+oo) with density exp(x).

ccfi_1.m,
defines points and weights for Boyd's quadrature rule
for [0,+oo) with density 1.

ccii_0.m,
defines points and weights for Boyd's quadrature rule
for (oo,+oo) with density exp(x^2).

ccii_1.m,
defines points and weights for Boyd's quadrature rule
for (oo,+oo) with density 1.

chebyshev1_compute.m
computes a GaussChebyshev type 1 quadrature rule.

chebyshev2_compute.m
computes a GaussChebyshev type 2 quadrature rule.

chebyshev3_compute.m,
computes a GaussChebyshev type 3 quadrature rule.

fejer1_compute.m,
computes a Fejer type 1 quadrature rule.

fejer2_compute.m,
computes a Fejer type 2 quadrature rule.

r8_factorial.m,
evaluates the factorial function.

r8_mop.m,
evaluates an integer power of 1 as an R8.

timestamp.m,
prints the current YMDHMS date as a time stamp.
Examples and Tests:

cc_project_test.m,
calls all the tests;

cc_project_test_output.txt,
the output file.

cardinal_cos_test.m,
plots a cardinal cosine interpolant basis function.

cardinal_cos.png,
a plot of a cardinal cosine interpolant basis function.

cardinal_sin_test.m,
plots a cardinal sine interpolant basis function.

cardinal_sin.png,
a plot of a cardinal sine interpolant basis function.

cardinal_test.m,
checks the Lagrange property for the cardinal cosine and sine
families.

ccff_asymptotic_test.m,
tests ccff_asymptotic() for a specific integrand.

ccff_tabulate.m,
tabulates CCFF quadrature rules for the Legendre integral.

ccfi_0_tabulate.m,
tabulates CCFI_0 quadrature rules for the Laguerre integral
with density exp(x).

ccfi_1_tabulate.m,
tabulates CCFI_1 quadrature rules for the Laguerre integral
with density 1.

ccii_0_tabulate.m,
tabulates CCII_0 quadrature rules for the Hermite integral
with density exp(x^2).

ccii_1_tabulate.m,
tabulates CCII_1 quadrature rules for the Hermite integral
with density 1.

compare_ff_test.m,
prints out the order 5 version of Boyd's ClenshawCurtis type
rule for the Legendre integral, comparing it with several other
rules.

legendre_exactness.m,
tests a quadrature rule for exactness on the Legendre integral.

legendre_integral.m,
returns the value of the Legendre integral of a monomial.

legendre_monomial_quadrature.m,
determines the error when a quadrature rule is applied to the
Legendre integral of a monomial.

legendre_test_integral.m,
returns the exact value of the Legendre integral of the
test integrand.

legendre_test_integrand.m,
evaluates a test integrand for the Legendre integral.
You can go up one level to
the MATLAB source codes.
Last modified on 25 May 2014.