ALGLIB, a simple symbol-manipulation package

ABSTRACT

ALGLIB—a library of procedures that perform analytic differentiation and other simple symbolic manipulations—has certain advantages over existing and more comprehensive packages. It can be implemented in a high-level language of the user's choice using a pseudocode available from the authors, and it is easily interfaced with the user's programs.

REFERENCES

• 1: Bailey. P.J., Cole, A.}.. and Morrison, R. Triplex user manual. CS/82/5. Dept. of Computational Science, Univ. of St. Andrew. N. Haugh, St. Andrew, Fife, Scotland. 1982.
• 2: Bogen. R.A., et al. MACSYMA reference manual. Version 6. Laboratory for Computer Science, M.I.T.. Cambridge, Mass., 1977.
• 3: Bohlender. G., et al. Matrix Pascal. Res. Rep. RC9577 (42297). IBM Research Division, Yorktown Heights, N.Y.. 1982.
• 4: A. J. Cole , R. Morrison, An Introduction to Programming with S-ALGOL, Cambridge University Press, New York, NY, 1982
• 5: J. E. Dennis, Jr. , Robert B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16), Soc for Industrial & Applied Math, 1996
• 6: Hearn. A. REDUCE 2 user's manual. Univ. of Utah, Salt Lake City. 1973.
• 7: Sandie Turner Jones, Searching for solutions of finite nonlinear systems -- an interval approach., 1978
• 8: Garth P. McCormick, Nonlinear programming: theory, algorithms, and applications, John Wiley & Sons, Inc., New York, NY, 1983
• 9: Moore, R.E.. and Jones, ST. Safe starting regions for iterative methods. SIAM \. Numer. Anal. 14.6 {Dec. 1977), 1051-1065.
• 10: Morrison, R., Cole, A.J.. Bailey, P.J., Wolfe, M.A.. and Shearer, J.M. Experience in using a high level language which supports interval arithmetic. In Proceedings of ARITH6, the 6th Symposium on Computer Arithmetic (Aarhus. Denmark, June 20-22). IEEE Computer Society Technical Committee on Computer Architecture. 1983, pp. 74-78.
• 11: Pugh, R.E. A language for nonlinear programming problems. Math. Progran?. 2 (1972). 176-206.
• 12: Rail, L.B. CompuWional Solution of Nonlinear Opernror Equations. Wiley, New York, 1969.
• 13: Rail. L.B. Applications of software for automatic differentiation in numerical computation. Computing Suppl. 2 (1980), 141-156.
• 14: Sisser. F.S. Computer-generated interval extensions of factorable functions and their derivatives. Int. \. Compuf. Math. 10 (1982), 327-336.
• 15: Sisser. F.S. Inverting an interval Hessian of a factorable function. Computing 29 (1982). 63-72.
• 16: Sisser. F.S. A modified Newton's method for minimizing factorable functions. 1. Optim. Theory Appl. 38, 4 (Dec. 1962), 461-482.
• 17: Watanabe, S. Hybrid manipulations for the solution of systems of nonlinear algebraic equations. RIMS, Kyoto University 19 (1983). 367-395.

INDEX TERMS

Classification:
  D. Software
  D.2 SOFTWARE ENGINEERING
      D.2.2 Design Tools and Techniques
          Subjects: Software libraries

  E. Data
  E.2 DATA STORAGE REPRESENTATIONS
      Subjects: Composite structures**

  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.1 Expressions and Their Representation
          Subjects: Representations (general and polynomial)
      I.1.3 Languages and Systems

          Nouns: ALGLIB

General Terms:
Design, Languages