John C. Nash
Abstract
Microcomputers, when properly programmed, have sufficient memory and speed to successfully perform serious calculations of modest size--linear equations, least squares, matrix inverse or generalized inverse, and the symmetric matrix eigenproblem.
- 1 Adler. A. Matrix inversion. Interface Age 4, 11 (Nov. 1979). 30-36. A discussion of matrix methods sadly dated even when published.Google Scholar
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- 9 Nash, J.C. Compacr Numerical Methods for Compurers: Linear Algebra and Function Minimization. John Wiley, New York, 1979. A discussion of problem types arising in the natural and social sciences that can be solved by linear algebra and function minimization methods. Step-and-description algorithms suitable for rapid implementation are included.Google Scholar
- 10 Nash J.C. Generalized inverse matrices: A practical tool for matrix methods on microcomputers. Interface Age 5, 9 (Sept. 1960). 32-37. A description of the first version of the package descfibed in this paper, mainly directed at unsophisticated users. Listings are included but so photoreduced that readers have had difficulties implementing the code from a keyboard.Google Scholar
- 11 Nash, J.C. and Shlien, S. Simple algorithms for the partial singular value decomposition. Work. Paper 83-27. Faculty of Administration, Univ. of Ottawa, Ontario. This paper, submitted for more general publication, includes a step-and-description algorithm of the streamlined singular value decomposition used in the package described in this paper.Google Scholar
- 12 Nash, J.C. LEQBO5 Documenfafion. Nash Information Services, Inc., Ottawa, Ontario, 1984. Documentation and source code of the package described in this paper.Google Scholar
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- 15 Wilkinson, J.H., and Reinsch. C., Eds. Handbookfor Automatic Conrpufation. Vol. 2. Linear Algebra. Springer-Verlag. New York, 1971. The "New Testament" of numerical linear algebra. incorporating ALGOL versions of many important methods for matrix computations.Google Scholar
Index Terms
- Design and implementation of a very small linear algebra program package
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Reviews
Ian Gladwell
This paper describes an attempt to provide a linear algebra package suitable for small microcomputers. Those linear algebra facilities which are implemented are a set of the most popular currently used on mainframes; that is, the solution of linear systems, linear least squares, and the symmetric eigenvalue problem. Memory is at a premium on small microcomputers, and so to provide all these facilities simultaneously an SVD algorithm is implemented as the underlying code for each requirement, exploiting features of BASIC to keep the code compact. By these means, the user's own time and the microcomputer's memory are used economically, whereas the (usually) less important microcomputer's actual computing time is lengthened to some extent, in comparison with the most efficient possible codes for each requirement. A nonlinear least squares algorithm, based on the repeated use of the linear least squares code, is also implemented.
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