Automated selection of mathematical software

Current approaches to recommending mathematical software are qualitative and categorical. These approaches are unsatisfactory when the problem to be solved has features that can “trade-off” in the recommendation process. A quantitative system is proposed that permits tradeoffs and can be built and modified incrementally. This quantitative approach extends other knowledge-engineering techniques in its knowledge representation and aggregation facilities. The system is demonstrated on the domain of ordinary differential equation initial value problems. The results are significantly superior to an existing qualitative (decision tree) system.

[1]  RICHARD 0. DUDA,et al.  Subjective bayesian methods for rule-based inference systems , 1899, AFIPS '76.

[2]  L. Zadeh.  The role of fuzzy logic in the management of uncertainty in expert systems , 1983 .

[3]  P. M. Hanson,et al.  Algorithm 687: a decision tree for the numerical solution of initial value ordinary differential equations , 1991, TOMS.

[4]  Michael Lucks.  A knowledge-based framework for the selection of mathematical software , 1990 .

[5]  Colin W. Cryer,et al.  NAXPERT: a prototype expert system for numerical software , 1988 .

[6]  A. D. Hall,et al.  The PORT Mathematical Subroutine Library , 1978, TOMS.

[7]  Ronald F. Boisvert,et al.  GAMS: a framework for the management of scientific software , 1985, TOMS.

[8]  Ian Gladwell,et al.  Initial Value Routines in the NAG Library , 1979, TOMS.

[9]  John R. Rice,et al.  The Algorithm Selection Problem , 1976, Adv. Comput..

[10]  D. E. Bell,et al.  Conflicting Objectives in Decisions , 1978 .

[11]  W. Silvert.  Symmetric Summation: A Class of Operations on Fuzzy Sets , 1979 .

[12]  P. W. Gaffney,et al.  Algorithm 606: NITPACK: An Interactive Tree Package , 1983, TOMS.

[13]  Ron Sacks-Davis,et al.  A review of recent developments in solving ODEs , 1985, CSUR.

[14]  Mohamed S. Kamel,et al.  ODEXPERT: an expert system to select numerical solvers for initial value ODE systems , 1993, TOMS.

[15]  R. L. Keeney,et al.  Decisions with Multiple Objectives: Preferences and Value Trade-Offs , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[16]  Edward H. Shortliffe,et al.  The Dempster-Shafer theory of evidence , 1990 .

[17]  P. W. Gaffney,et al.  NEXUS: towards a problem solving environment (PSE) for scientific computing , 1986, SGNM.