Performance evaluation of programs for certain Bessel functions

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Performance evaluation of programs for certain Bessel functions

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 15 , Issue 1 (March 1989) table of contents

Pages: 41 - 48

Year of Publication: 1989

ISSN:0098-3500

Authors

W. J. Cody	Argonne National Lab, Argonne, IL
L. Stoltz	Argonne National Lab, Argonne, IL

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 4, Downloads (12 Months): 24, Citation Count: 4

Additional Information:

abstract references cited by index terms review collaborative colleagues

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ABSTRACT

This paper presents methods for performance evaluation of the K Bessel functions. Accuracy estimates are based on comparisons involving the multiplication theorem. Some ideas for checking robustness are also given. The techniques used here are easily extended to the Y Bessel functions and, with a little more effort, to the I and J functions. Details on a specific implementation for testing the K Bessel functions are included.

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	Milton Abramowitz, Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,, Dover Publications, Incorporated, 1974
	2	CAMPBELL, J.B. A FORTRAN IV subroutine for the modified bessel functions of the third kind of real order and real argument. Report NRC/ERB-925, National Research Council, Canada, 1980.
	3	CODY, W.J. SPECFUN--a portable special function package. In New Computing Environments: Microcomputers in Large-Scale Scientific Computing. A. Wouk, ed. SIAM, Philadelphia, 1987, pp. 1-12.
	4	W. J. Cody, Algorithm 665: Machar: a subroutine to dynamically determined machine parameters, ACM Transactions on Mathematical Software (TOMS), v.14 n.4, p.303-311, Dec. 1988 [doi>10.1145/50063.51907]
	5	William James Cody, Software Manual for the Elementary Functions (Prentice-Hall series in computational mathematics), Prentice-Hall, Inc., Upper Saddle River, NJ, 1980
	6	DONGARRA, J. J., AND DU CROZ, J. Distribution of mathematical software via electronic mail. Tech. Rep. MCS-TM-48, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., 1985.
	7	SFUN/LIBRARY User's Manual. IMSL, Inc., Houston, Tex., 1987.

CITED BY 4

	W. J. Cody, Performance evaluation of programs for the error and complementary error functions, ACM Transactions on Mathematical Software (TOMS), v.16 n.1, p.29-37, March 1990
	W. J. Cody , L. Stoltz, The use of Taylor series to test accuracy of function programs, ACM Transactions on Mathematical Software (TOMS), v.17 n.1, p.55-63, March 1991
	W. J. Cody, Algorithm 715; SPECFUN—a portable FORTRAN package of special function routines and test drivers, ACM Transactions on Mathematical Software (TOMS), v.19 n.1, p.22-30, March 1993
	W. J. Cody, Performance evaluation of programs related to the real gamma function, ACM Transactions on Mathematical Software (TOMS), v.17 n.1, p.46-54, March 1991

INDEX TERMS

Primary Classification:
G. Mathematics of Computing
G.4 MATHEMATICAL SOFTWARE
Subjects: Certification and testing

Additional Classification:
G. Mathematics of Computing
G.1 NUMERICAL ANALYSIS
G.1.0 General
Subjects: Numerical algorithms
G.4 MATHEMATICAL SOFTWARE
Subjects: Reliability and robustness

General Terms:
Algorithms, Performance, Reliability, Verification

REVIEW

"Ian Gladwell : Reviewer"

This paper considers the testing of programs for evaluating the K Bessel functions of real argument and index. It is argued that the code for evaluating the K functions is not likely to be based on the use of the well-known more...

Collaborative Colleagues:

W. J. Cody: colleagues

L. Stoltz: colleagues

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