John C. Nash's practical guide to small-memory algorithms for linear algebra, least squares, and function minimisation — the methods that made numerical computing feasible on small computers of the 1970s and 1980s and which continue to inform the R numerical libraries. Arnold maintained a support area with Fortran, Pascal, and later R implementations of the methods described.
The text walks through compact algorithms for the standard problems of scientific computing: solving systems of linear equations, computing the singular-value decomposition, finding eigenvalues, fitting linear and non-linear least squares, and minimising a smooth function of several variables using Newton, quasi-Newton and conjugate-gradient methods. The presentation emphasises numerical robustness and bounded memory rather than peak performance.
John C. Nash carried the methods forward into the R era, maintaining the optimx and nlmrt packages on CRAN and serving as a book-review editor for the R Journal. The Arnold-hosted support pages distributed Pascal, Fortran and later R ports of the algorithms, linking classical numerical analysis to reproducible statistical software practice.
About the author
John C. Nash— Professor Emeritus of Management Science
Numerical & Statistical Computing · 1947–
Affiliations: Telfer School of Management, University of Ottawa — retired faculty in analytics and computational economics · R Core / CRAN — maintainer of the optimx and nlmrt packages and contributor to nonlinear optimisation documentation
Intended audience
- scientific programmers
- numerical analysts
- engineers writing computational code
Subject classification
- Numerical analysis
- Scientific computing
- Linear algebra algorithms
Scope
- linear algebra
- least squares
- function minimisation
- eigenvalue problems
Edition history
- First published
- 1979
- Imprint
- Adam Hilger / Edward Arnold
Bibliographic details
| Format | ISBN | Year | Notes |
|---|---|---|---|
| 2nd edition, illustrated | 0852743181 | 1990 | Google Books bibliographic metadata. |
| 2nd edition, illustrated | 9780852743188 | 1990 | Google Books bibliographic metadata. |
Source notes
- Google Books bibliographic record — Confirms 2nd edition (1990), publisher line and ISBN pair.
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Frequently asked
- Which programming languages does the book cover?
- Successive Arnold editions carried Fortran source for each algorithm, Pascal translations for teaching contexts, BASIC implementations of the most compact algorithms for microcomputer use, and R implementations added in later revisions.
- How does the book relate to the optimx R package?
- Many of the optimisation algorithms covered in Compact Numerical Methods are also packaged in the optimx R package (J. C. Nash and colleagues) on CRAN, which packages modern variants of the routines for use in current R workflows.
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