Page 26 - Compact Numerical Methods For Computers

16 Compact numerical methods for computer

and specialisation to one programming language would have inhibited users of these
special machines. Now, however, computer users are unlikely to be willing to type in
code if a machine-readable form of an algorithm exists. Even if the programming
language must be translated. having a workable form is useful as a starting point.
The original codes for the first edition were in BASIC for a Data General NOVA.
Later these codes were made to run on a North Star Horizon. Some were made to
work on a Hewlett-Packard 9830A. Present BASIC versions run on various common
microcomputers under the Microsoft BASIC dialect; however, since I have used very
conservative coding practices, apart from occasional syntactic deviations, they
conform to IS0 Minimal BASIC (IS0 6373-1984).
Rather than proof-reading the algorithms for the first edition, I re-coded them in
FORTRAN. These codes exist as NASHLIB, and were and are commercially available
from the author. I have not, however, been particularly satisfied that the FORTRAN
implementation shows the methods to advantage, since the structure of the algor-
ithms seems to get lost in the detail of FORTRAN code. Also, the working parts of the
codes are overshadowed by the variable definitions and subroutine calls. Compact
methods are often best placed in-line rather than called as standard subprograms as I
have already indicated.
In the current edition, I want to stay close to the original step-and-description
form of the algorithms, but nevertheless wish to offer working codes which could be
distributed in machine-readable form. I have chosen to present the algorithms in
Borland Turbo Pascal. This has the following justification.
(i) Pascal allows comments to be placed anywhere in the code, so that the
original style for the algorithms, except for the typographic conventions, could be
kept.
(ii) Turbo Pascal is available for many machines and is relatively inexpensive. It
is used as a teaching tool at many universities and colleges, including the University
of Ottawa. Version 3.01a of the Turbo Pascal system was used in developing the
codes which appear here. I intend to prepare versions of the codes to run under later
versions of this programming environment.
(iii) The differences between Turbo and Standard Pascal are unlikely to be
important for the methods, so that users of other Pascal compilers can also use these
codes.
(iv) Pascal is ‘close enough’ to many other programming languages to allow for
straightforward translation of the codes.
A particular disadvantage of Turbo Pascal for my development work is that I have
yet to find a convenient mechanism allowing automatic compilation and execution of
codes, which would permit me to check a complete set of code via batch execution.
From the perspective of the physical length of the listings, the present algorithms are
also longer than I would like because Pascal requires program headings and
declarations. In the procedural parts of the codes, ‘begin’ and ‘end’ statements also
add to the line count to some extent.
From the user perspective, the requirement that matrix sizes be explicitly specified
can be a nuisance. For problems with varying matrix sizes it may be necessary to
compile separate versions of programs.