A web-based library for testing performance of numerical software for solving nonlinear algebraic equations

Mordechai Shacham, Neima Brauner, Michael B. Cutlip

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


An extensive test problem library of nonlinear algebraic equations (NLE) has been created and implemented on the World Wide Web. This web-based test problem library contains complete problem descriptions with the following information: the model equations in the same form as the input for the numerical solver, the explicit definitions of constraints on the variables, the initial estimates and function values at the initial estimates, and the variable values and function values at the solution. All variables and function values are reported with the full precision of the numerical solution. This library improves upon existing test problem collections regarding the type of information included and the form in which this information is stored and presented. The NLE library can be accessed through the Web site: http://www.polymath-software.com/library. It contains presently over 70 problems of various dimensions on lower, average, and higher difficulty levels. Some of the problems exhibit multiple solutions in the feasible and/or the infeasible subspaces, discontinuities, and false solutions that are identified as true solutions by most numerical solvers. This library can be of significant benefit to users and developers of NLE solvers for verifying the robustness and reliability of NLE solvers.

Original languageEnglish
Pages (from-to)547-554
Number of pages8
JournalComputers and Chemical Engineering
Issue number4-5
StatePublished - 15 May 2002


  • Nonlinear algebraic equations
  • Root finding
  • Test problem library

ASJC Scopus subject areas

  • General Chemical Engineering
  • Computer Science Applications


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