Computing hyperelliptic integrals for surface measure of ellipsoids

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Computing hyperelliptic integrals for surface measure of ellipsoids

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 20 , Issue 4 (December 1994) table of contents

Pages: 413 - 426

Year of Publication: 1994

ISSN:0098-3500

Authors

Charles F. Dunkl	Univ. of Virginia, Charlottesville
Donald E. Ramirez	Univ. of Virginia, Charlottesville

Publisher

ACM New York, NY, USA

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ABSTRACT

An algorithm for computing a class of hyperelliptic integrals and for determining the surface measure of ellipsoids is described. The algorithm is used to construct an omnibus optimal-design criterion.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	CARLSON, B. C. 1977. Special Functions of Applied Mathematics. Academic Press, New York.
	2	CARLSON, B. C. 1972. Int~grandes ~ deux formes quadratiques. C. R. Acad. Soc. Paris 274, 15, 1458-1461.
	3	CARLSON, B. C. 1966. Some inequalities for hypergeometric functions. Proc. Amer. Math. Soc. 17, 1, 32-39.
	4	CARLSON, B. C. 1963. Lauricella's hypergeometric function FD. J. Math. Anal. Appl. 7. 3, 452-470.
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	8	Charles F. Dunkl , Donald E. Ramirez, Algorithm 736; hyperelliptic integrals and the surface measure of ellipsoids, ACM Transactions on Mathematical Software (TOMS), v.20 n.4, p.427-435, Dec. 1994 [doi>10.1145/198429.198431]
	9	EXTON, H. B. 1976. Multtple Hypergeometric Functtons and Appltcattons. Halsted Press, New York.
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	13	SILVEY, S. D. AND TITTERINGTON, D. H. 1973. A geometric approach to optimal design theory. B~ometrtka 60, 1, 21-32.
	14	SRIVASTAVA, ~-~. M. AND KARLSSON, P. W. 1985. Multtple Gaussian Hypergeometric Series. Halsted Press, New York.
	15	WARDROP, n. AND MYERS, a. 1990. Some response surface designs for finding optimal conditions. J. Star. Plann. Inference 25, 1, 7-28.