Abstract
A methodology for mathematical software testing is presented which is applicable to classes of approximation and optimisation software. For testing purposes, a software implementation of an algorithm is regarded as a “black box”. Reference data sets are input to the software, and the results provided are compared with reference results. It is described how reference data sets and results can be generated using a data generator software which, when given reference results a priori produces reference data sets corresponding to them. The emphasis is on least-squares software, but the concepts have broader application. Factors affecting comparison are considered and quality metrics for quantifying performance of the software under test described.
Chapter PDF
Similar content being viewed by others
Keywords
References
Anthony, G. T., Butler, B. P., Cox, M. G., Forbes, A. B., Hannaby, S. A., Harris, P. M., Bittner, B., Drieschner, R., Elligsen, R., Gross, H. and Kok, J. (1993) Chebyshev reference software for the evaluation of coordinate measuring machine data. Technical Report EUR 15304 EN, National Physical Laboratory, Teddington, UK. Published on behalf of Commision of the European Communities.
Boggs, P. T., Byrd, R. H. and Schnabel, R. B. (1987) A stable and efficient algorithm for nonlinear orthogonal distance regression. J. Sci. Stat. Comput., 8 (6), 1052–1078.
Butler, B. P., Cox, M. G., Forbes, A. B., Hannaby, S. A., Harris, P. M. and Hodson, S. M. (1996) Statistics Software Qualification: Reference Data Sets. Royal Society of Chemistry, London. Edited by M. G. Cox, W. A. Hardcastle and S. L. R Ellison. In press.
Clenshaw, C. W. and Hayes, J. G. (1965) Curve and surface fitting. J. Inst. Math. Appl., 1, 164–183.
Cox, M. G. and Forbes, A. B. (1992) Strategies for testing form assessment software. Technical Report DITC 211/92, National Physical Laboratory, Teddington, UK.
Ellison, S. L. R., Cox,M. G., Forbes, A. B., Butler, B. P., Hannaby, S. A., Harris, P. M. and Hodson, Susan M. (1994) Development of data sets for the validation of analytical instrumentation. J. AOAC International, 77, 777–781.
Ford, B., Bentley, J., du Croz, J. J. and Hague, S. J. (1979) The NAG Library ‘machine’. Software–Practice and Experience, 9, 56–72.
Gentleman, W. M. and Marovich, S. B. (1974) More on algorithms that reveal properties of floating point arithmetic units. Comm. Ass. Comput. Mach., 17, 276–277.
Gill, P. E., Murray, W. and Wright, M. H. (1981) Practical Optimization. Academic Press, London.
Golub, G. H. and Van Loan, C. F. (1983) Matrix Computations. North Oxford Academic, Oxford.
Higham, N. J. (1997) Testing the correctness of linear algebra software, in The Quality of Numerical Software: Assessment and Enhancement (ed. R. F. Boisvert ), Chapman & Hall, London. (this volume)
Lyness, J. N. (1979) Performance profiles and software evaluation, in L. D. Fosdick, editor, Performance Evaluation of Numerical Software, Amsterdam. North-Holland, 51–58.
The Numerical Algorithms Group Limited (1996) The NAG Fortran Library, Mark 17. Wilkinson House, Jordan Hill Road, Oxford, 0X2 8DR, UK.
Snyder, W. Van (1997) Testing functions of one and two arguments, in The Quality of Numerical Software: Assessment and Enhancement (ed. R. F. Boisvert ), Chapman & Hall, London. (this volume)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 IFIP International Federation for Information Processing
About this chapter
Cite this chapter
Butler, B., Cox, M., Forbes, A., Hannaby, S., Harris, P. (1997). A methodology for testing classes of approximation and optimization software. In: Boisvert, R.F. (eds) Quality of Numerical Software. IFIP Advances in Information and Communication Technology. Springer, Boston, MA. https://doi.org/10.1007/978-1-5041-2940-4_10
Download citation
DOI: https://doi.org/10.1007/978-1-5041-2940-4_10
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-5041-2942-8
Online ISBN: 978-1-5041-2940-4
eBook Packages: Springer Book Archive