December 1960 - Vol. 3 No. 12

Numerical techniques are presented for computing the roots of polynomial equations. By applying the recommended scaling and inversion rules, the basic Bistrow and Newton-Raphson iterative techniques can be applied with great reliability. Both a high degree of accuracy and rapid convergence are realized. Numerical examples are shown to illustrate the pitfalls and to show how these are circumvented by application of the recomended procedures.

In reference to the discussion about evaluation ex on page 500 of the September Communications of the ACM, may I point out that there is no need to use Mr. Berin's lengthy expressions to obtain relation (9). If we use the simple formula (5) for x/2 and divide by the same formula for - x/2, we get (9) immediately.

An important property of the Newell Shaw-Simon scheme for computer storage of lists is that data having multiple occurrences need not be stored at more than one place in the computer. That is, lists may be “overlapped.” Unfortunately, overlapping poses a problem for subsequent erasure. Given a list that is no longer needed, it is desired to erase just those parts that do not overlap other lists. In LISP, McCarthy employs an elegant but inefficient solution to the problem. The present paper describes a general method which enables efficient erasure. The method employs interspersed reference counts to describe the extent of the overlapping.

In some logical problems it is necessary or convenient to invert the bit structure of a word, i.e., replace bit i by bit n + 1 - i for i = 1, 2, ···, n, thus creating a mirror image. The method described here exploits the CAQ instruction of the IBM 709 (or 7090) to accomplish such an inversion rapidly (n = 36).

The discrete flow systems discussed are characterized by the movement of randomly arriving items along interacting channels. Programming a digital computer to simulate such systems utilizes some techniques not common in other approaches to physical problems. The principal portion of the paper is a discussion of two simulation studies that illustrate some of the programming problems involved. One is of an extensive package-handling plant, with the objective being optimization of parameters such as storage capacities and processing rates. In the other, air traffic flow and control procedures are simulated to compare the effects of alternative control decisions.

Each year electronic computers become more sophisticated, and the programs they must process become more complex. Because of this, dependence of those in computing on the skill and experience of operators is increasing. At the same time, selection and training of qualified operators grows more difficult. To meet the need for a quick, accurate, uniform operator test and training aid, the authors have developed COPE (Console Operator Proficiency Examination), outlined below While this examination is programmed specifically for the IBM 705 Mode II with two Tape Record Coordinators, similar programs could be developed for other computers.

An evaluation of an automatic programming method can be made from many points of view. Two recent articles give evaluations of two compilers for the IBM 650 based on the method of decomposition of compiler statements into machine language [1, 2]. This paper briefly describes these two compilers, appraises them for the ease with which they can be used and for the efficiency of the programs they produce. While this approach is of less theoretical interest than the evaluations presented in the referenced articles, it is of substantially more practical significance to a programmer or to an installation which is seeking to answer the following questions: Should a compiler be used? If so, which compiler? It will be noted that no universal answers are possible since such factors as relative costs and availability of machine time and programmer time, the skill and predilections of programmers, and the type of problems are of major importance. Nevertheless, the results presented below, we believe, provide the best available guide for arriving at reasonable answers.