Performance evaluation of programs for certain Bessel functions

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

• 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.

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