Quadrature subroutines for splines and B-splines. [BFQUAD, BSQUAD, PFQUAD, and PPQUAD]
The B-spline package of De Boor numerically manipulates B-splines in a variety of ways. Notably absent from the package are routines for integrating B-splines. To cover this deficiency BSQUAD, PPQUAD, BFQUAD, and PFQUAD for integrating splines and B-splines were constructed and are described herein. BSQUAD accepts the B-representation in terms of the knot array T(*), the coefficient array BCOEF(*), the number of coefficients N, and the order K to compute integrals on subintervals of T(K) less than or equal to X less than or equal to T(N + 1). Distinct knots partition the interval of integration so that polynomial integration by a Gauss quadrature formula can be implemented. The piecewise polynomial (PP) representation, although not preferred over the B-representation for solving problems, is sometimes needed, and the De Boor package has a routine to make the conversion. This PP form is accepted by PPQUAD, which sums polynomial evaluations of integrals on the partition. More general integrals for the product of a function f(x) and a B-spline are computed similarly in subroutines BFQUAD and PFQUAD using a quadrature routine with error control and a code structure similar to that in BSQUAD and PPQUAD.
- Research Organization:
- Sandia Labs., Albuquerque, NM (USA)
- DOE Contract Number:
- EY-76-C-04-0789
- OSTI ID:
- 5724915
- Report Number(s):
- SAND-79-1825
- Country of Publication:
- United States
- Language:
- English
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