The Necessity of Publishing Programs

A major reason for publication of programs for numerical algorithms is that no publication results in little or no use of the algorithm. In the experience of the author, the typical non-trivial numerical algorithm cannot be implemented by the typical numerical analyst in the same field, let alone a typical programmer or computer user. For example, a substantial number of algorithms for Chebyshev and Li approximation make use of linear programming. Potential consumers with no knowledge of linear programming are out of luck. Worse still, the algorithms are usually so vaguely stated that even those who know some linear programming are unsure how the algorithm can be implemented and, in particular, implemented in an efficient and effective manner. An instructive example is the differential correction (DC) algorithm of Cheney and Loeb for rational Chebyshev approximation.' The authors state that the key minimization can be done by linear programming (see Ref. 1, p. 74). Although the author has taught use of linear programming, he was unable to see how it could be applied: thus an expert in linear programming is required to implement the DC algorithm. The first published program for DC only appeared in 1975 by Kaufman and Taylor. To emphasize the difficulty of the linear programming phase of DC, (i) those authors soon had to revise their published code, and (ii) work by Barrodale et al. (1977) suggested that the 1975 program was neither as fast as possible nor particularly reliable. Kaufman, Leeming, and Taylor have since then again revised their DC program. This illustrates the difficulty of implementation.