Numerical analysis using nonprocedural paradigms

ABSTRACT

This article presents a survey on the innovative features of a handful of languages that offer new features that can be valuable in numerical analysis, and a survey of the pros and cons of the languages with regards to work in numerical analysis. Language features such as polymorphism, first-class functions, and object-oriented programming offer improved writability, readability, reliability, and maintenance of computer software. The article discusses language features and uses, and includes a comparison of current implementations. It is intended both as an introduction to nonprocedural language features for persons working in numerical mathematics and as an exploration of some of the language requirements of numerical mathematics for persons working in language development. The article discusses C++, Fortran 77, Fortran 90, Haskell, Lisp/CLOS, Modula-3, Sather, and SML with respect to a variety of numerical analysis tasks: interpolation, optimization, array access and update, iteration, recursion, random number generation, and Gaussian elimination on sparse matrices.

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

Additional Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.3 Languages and Systems
          Subjects: Nonprocedural languages**

General Terms:
Languages

Keywords:
Gaussian elimination, benchmarks, experimental languages, linear algebra, programming languages, sparse matrices