Program verification in the presence of complex numbers, functions with branch cuts etc

James H. Davenport, Russell Bradford, Matthew England, David Wilson

Research output: Chapter in Book/Report/Conference proceedingConference proceeding

25 Citations (Scopus)
6 Downloads (Pure)

Abstract

In considering the reliability of numerical programs, it is normal to ''limit our study to the semantics dealing with numerical precision'' (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that essentially ignores the numerics. The thesis of this paper is that there is a class of problems that fall between these two, which could be described as ''does the low-level arithmetic implement the high-level mathematics''. Many of these problems arise because mathematics, particularly the mathematics of the complex numbers, is more difficult than expected: for example the complex function log is not continuous, writing down a program to compute an inverse function is more complicated than just solving an equation, and many algebraic simplification rules are not universally valid. The good news is that these problems are theoretically capable of being solved, and are practically close to being solved, but not yet solved, in several real-world examples. However, there is still a long way to go before implementations match the theoretical possibilities.

Original languageEnglish
Title of host publicationProceedings - 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2012
PublisherIEEE
Pages83-88
Number of pages6
ISBN (Print)9780769549347
DOIs
Publication statusPublished - 2012
Externally publishedYes
Event14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2012 - Timisoara, Romania
Duration: 26 Sep 201229 Sep 2012

Conference

Conference14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2012
CountryRomania
CityTimisoara
Period26/09/1229/09/12

Bibliographical note

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Keywords

  • algebra
  • branch cut
  • singularity
  • Verification

ASJC Scopus subject areas

  • Applied Mathematics
  • Numerical Analysis

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  • Cite this

    Davenport, J. H., Bradford, R., England, M., & Wilson, D. (2012). Program verification in the presence of complex numbers, functions with branch cuts etc. In Proceedings - 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2012 (pp. 83-88). [6481015] IEEE. https://doi.org/10.1109/SYNASC.2012.68