Compact Numerical Methods for Computers

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.