Algorithm 736: Hyperelliptic integrals and the surface measure of ellipsoids

ABSTRACT

The algorithm for computing a class of hyperelliptic integrals and for determining the surface measure of ellipsoids is described in detail by Dunkl and Ramirez [1994]. An efficient implementation of their algorithm is presented here.

REFERENCES

• 1: CARLSON, B. C. 1963. Laurmella's hypergeometric function FD. J. Math. Anal. Appl. 7, 3, 452 470.
• 2: DAVIS, P. J. AND RAmNOWITZ, P 1984. Methods of Numerical Integration. 2nd ed. Academic Press, Orlando, Fla.
• 3: DUNKL, C. F. 1962. Romberg quadrature to prescribed accuracy. SHARE File 7090-1481, TYQUAD.
• 4: Charles F. Dunkl , Donald E. Ramirez, Computing hyperelliptic integrals for surface measure of ellipsoids, ACM Transactions on Mathematical Software (TOMS), v.20 n.4, p.413-426, Dec. 1994 [doi>10.1145/198429.198430]
• 5: KAH~, W. M. 1980. Handheld calculator evaluates integrals. Hewlett-Packard J. 31, 8, 23-32.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.4 Quadrature and Numerical Differentiation
          Subjects: Multidimensional (multiple) quadrature

Additional Classification:
  G. Mathematics of Computing

General Terms:
Algorithms

Keywords:
Lauricella's hypergeometric function, elliptic integral, expected radius, surface measure