Numerical Evaluation of Special Functions
D. W. Lozier and F. W. J. Olver
6. Testing and Library Construction
In this section we list articles and books that provide general
observations on the testing of software and/or the construction
of software libraries for the special functions.
For information on individual libraries see § 3.
[ Cod74]
,
[ Cod76]
,
[ Cod82]
,
[ Cod84b]
,
[ Cod85]
,
[ CS91]
,
[ Eva74, especially pp. 275--301 and 357--435]
,
[ Ful77]
,
[ Gaf88]
,
[ Kuk71]
,
[ LMS73a]
,
[ LMS73b]
,
[ Mos89]
,
[ PTVF92, example books]
,
[ Ric83]
,
[ Sch76]
,
[ SL73]
.
References
- Cod74
-
W. J. Cody, The construction of numerical subroutine libraries, SIAM Rev.
16 (1974), 36--46.
- Cod76
-
W. J. Cody, An overview of software development for special functions,
Lecture Notes in Mathematics 506: Numerical Analysis Dundee, 1975 (G. A.
Watson, ed.), Springer-Verlag, Berlin, 1976, pp. 38--48.
- Cod82
-
W. J. Cody, Implementation and testing of function software, Lecture
Notes in Computer Science No. 142. Problems and Methodologies in
Mathematical Software Production (P. C. Messina and A. Murli, eds.),
Springer-Verlag, Berlin, 1982, pp. 24--47.
- Cod84
-
W. J. Cody, Observations on the mathematical software effort, Sources and
Development of Mathematical Software (W. R. Cowell, ed.), Prentice-Hall,
Inc., Englewood Cliffs, New Jersey, 1984, pp. 1--19.
- Cod85
-
W. J. Cody, Software for special functions, Rend. Sem. Mat. Univ.
Politec. Torino Fascicolo Speciale. Special Functions: Theory and
Computation (1985), 91--116.
- CS91
-
W. J. Cody and L. Stoltz, The use of Taylor series to test accuracy of
function programs, ACM Trans. Math. Software 17 (1991), 55--63.
- Eva74
-
D. J. Evans (ed.), Software for numerical mathematics, Proceedings of the
Loughboro University of Technology Conference of the IMA held in April 1973,
Academic Press, London, 1974.
- Ful77
-
L. W. Fullerton, Portable special function routines, Lecture Notes in
Computer Science 57: Portability of Numerical Software (Oak Brook 1976)
(W. R. Cowell, ed.), Springer-Verlag, Berlin, 1977, pp. 452--483.
- Gaf88
-
P. W. Gaffney, When things go wrong , Pitman Research Notes in
Mathematics Series (D. F. Griffiths and G. A. Watson, eds.), vol. 170,
Longman Scientific and Technical, Harlow, Essex, U. K., 1988, pp. 67--114.
- Kuk71
-
H. Kuki, Mathematical function subprograms for basic system libraries---
objectives, constraints and trade-off, Mathematical Software (J. R. Rice,
ed.), Academic Press, New York, 1971, pp. 187--199.
- LMS73a
-
D. W. Lozier, L. C. Maximon, and W. L. Sadowski, A bit comparison program
for algorithm testing, Comput. J. 16 (1973), 111--117.
- LMS73b
-
D. W. Lozier, L. C. Maximon, and W. L. Sadowski, Performance testing of a
Fortran library of mathematical function routines---A case study in the
application of testing techniques, J. Res. Nat. Bur. Standards 77B
(1973), 101--110.
- Mos89
-
S. L. B. Moshier, Methods and programs for mathematical functions, Ellis
Horwood Limited, Chichester, 1989, separate diskette.
- PTVF92
-
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery,
Numerical recipes. The art of scientific computing, second ed., Cambridge
University Press, 1992, diskettes and example books available. Editions exist
in Basic (1991), C (1992), Fortran (1992), Macintosh Fortran (1988) and
Pascal (1989).
- Ric83
-
J. R. Rice, Numerical methods, software and analysis : IMSL
reference edition, McGraw-Hill Book Company, New York, 1983.
- Sch76
-
J. L. Schonfelder, The production of special function routines for a
multi-machine library, Software---Practice and Experience 6
(1976), 71--82.
- SL73
-
W. L. Sadowski and D. W. Lozier, A unified standards approach to algorithm
testing, Program Test Methods (W. C. Hetzel, ed.), Prentice-Hall, Inc.,
Englewood Cliffs, New Jersey, 1973, pp. 277--290.
Abstract:
This document is an excerpt from the current hypertext version of
an article that appeared in Walter Gautschi (ed.),
Mathematics of Computation 1943--1993: A Half-Century of
Computational Mathematics, Proceedings of Symposia in
Applied Mathematics 48, American Mathematical Society,
Providence, RI 02940, 1994.
The symposium was held at the University of British Columbia
August 9--13, 1993, in honor of the fiftieth anniversary of
the journal Mathematics of Computation.
The original abstract follows.
Higher transcendental functions continue to play varied and
important roles in investigations by engineers, mathematicians,
scientists and statisticians.
The purpose of this paper is to assist in locating useful approximations
and software for the numerical generation of these functions, and to
offer some suggestions for future developments in this field.
Applied and Computational Mathematics Division,
National Institute of Standards and Technology,
Gaithersburg, Md 20899
E-mail address: dlozier@nist.gov
Institute for Physical Science and Technology,
University of Maryland,
College Park, MD 20742
E-mail address: olver@bessel.umd.edu
The research of the second author has been supported by NSF
Grant CCR 89-14933.
1991 Mathematics Subject Classification. Primary 65D20;
Secondary 33-00.
Daniel W Lozier
Fri Apr 7 14:27:57 EDT 1995