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Software Test System for Special Functions

D.W. Lozier, M.A. McClain, and F.W.J. Olver, ACMD

The early as well as the current literature in computer science, such as the publications of the ACM, shows that computer subroutines for numerically evaluating special functions are of great interest. This is a natural reflection of the importance of special functions in applied mathematics, which has existed since the great 19th century developments in mathematics and the mathematization of physics. Whereas previously methods associated with special functions were just about the only way of obtaining solutions to nontrivial problems, the vast increases in computational power brought about by technology have led to highly effective methods based on discretization and iteration. Special functions remain centrally important in the computationally efficient representation of solutions to continuous problems, and in the experimental verification of computer programs that implement the newer methods of solution.

As with all computer software, the problem of correctness needs to be addressed. For special functions, the wealth of mathematical knowledge coupled with the latest computer technology in communications and parallel processing provides a special opportunity to develop highly effective test methods. The mathematical interests and capabilities of ACMD, together with the comprehensive computer base in NIST, opens the possibility for an important advance in computer software testing.

Dr. Lozier presented a prospectus for an Internet-based test service at the Fall 1995 SIAM minisymposium devoted to computational issues in special functions. The service would consist of three key components:

Reference Software
Highly accurate and reliable, but not necessarily highly efficient, software for generating high-precision numerical values (and, eventually, interval inclusions) over very extensive argument ranges.
Comparison Software
Realistic, interval-based assessments of functional accuracy, or numerical precision, will be employed to avoid the sometimes unrealistic measures based on conventional absolute and relative error.
Communications Interface
Test requests and test results will be accepted and returned over the Internet through use of appropriately designed World Wide Web documents.
The proposed Service will be unlike any prior test procedure for special functions in that it will offer users a highly structured environment in which tests can be tailored specifically to a particular application. Progress is being made in working out the mathematical foundation and the programming requirements of the project, and a prototype system is expected to be operational in the next few months.

next up previous
Next: Development of SLI Up: Testing and Evaluation Previous: The Matrix Market

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