Search

Presents comments and suggestions for the publication the journal "Communications of the ACM." Proposition for the publication of papers; Criticisms on the article of Peter Naur in the December 1975 issue entitled "Programming Languages, Natural Languages, and Mathematics"; Comments on the contribution of Wallace E. Lin in the January 1976 issue.

The article provides information on the upcoming symposiums related to the computer engineering in 1966. A one-day symposium will be sponsored by ACM, SIAM and Florida State University on March 14 on "The Recommended Impact of Computer Applications on the Undergraduate Mathematics Curriculum." The four New York Metropolitan Area chapters will hold a one-day symposium in New York City on March 18. A session of invited papers will be devoted to "The Application of Computers to the Problems of a Metropolitan Society." In addition, a session of contributed papers on any topics in the computer field is now in the process of being organized . Automatic Data Processing exhibits and workshops headline the Federal Government Accountants Association 15th National Symposium, in Minneapolis, June 15-17. Topics include "Case Studies in ADP," "Programming: The Modern Budget Officer's Tool," and "The Future of Computers in the Federal Government." The Instrument Society of America (ISA) has invited papers for presentation at the 21st Annual ISA Conference and Exhibit, to be conducted October 24-27 in New York City. Theme of the meeting is "Instrumentation for an Urban Society."

This paper provides performance results using the SPERRY UNIVAC 1100 Series linear programming product FMPS to solve a set of 16 real-world linear programming problems. As such, this paper provides a data point for the actual performance of a commercial simplex algorithm on real-world linear programming problems and shows that the simplex algorithm is a linear time algorithm in actual performance. Correlations and performance relationships not previously available are also provided. [ABSTRACT FROM AUTHOR]

The article presents a list of upcoming symposiums on computer science and technology in the U.S. Texas A&M Instrumentation Symposium for the Process Industries will be held in Texas University on January 19-21, 1966. The American Mathematical Society Annual Meeting, cosponsored by the Mathematics Association of America, will be held in Chicago, Illinois, on January 24-28, 1966. The 1966 Annual Symposium on Reliability will be held at the Sheraton-Palace Hotel, San Francisco, California, on January 25-27, 1966. The International Symposium on Information Theory will be held at the University of California, Los Angeles, on January 31-February 3, 1966. The 6th Annual Computing Center Conference, ACM-SIAM-FSU Symposium will held on March 12-19, 1966 at Florida State University, Tallahassee. The Symposium on Simulation Languages will be held on March 17-18, 1966, at the University of Pennsylvania, Philadelphia. The 4th International ISA Aerospace Instrumentation Symposium will be held at the College of Aeronautics, Cranfield, England, on March 21-25, 1966.

The article presents a conversation with educationists Seymour Papert, Marvin Minsky and Alan Kay on educational reform, artificial intelligence, computer science and human-computer interaction. The importance of the computer is how you learn mathematics, and how it allows children to think about powerful ideas in mathematics. Children are capable of learning plenty more mathematics than anyone gives them credit for with or without a computer. The most important thing in learning is copying how other people think. The way to learn something hard is by getting new ideas. Programming is the most powerful medium of developing the sophisticated and rigorous thinking needed for mathematics, for grammar, for physics, for statistics, and all the hard subjects. Programming should be a key part of the intellectual development of people growing up. The idea of programming itself is something in evolution so it will not mean exactly what it is thought to mean.

Numerical mathematics is viewed as the analysis of continuous algorithms. Four of the components of numerical mathematics are discussed. These are: foundations (finite precision number systems, computational complexity), synthesis and analysis of algorithms, analysis of error, programs and program libraries. [ABSTRACT FROM AUTHOR]

The article presents abstracts of some of the papers that were published in the "Journal of the Association for Computing Machinery." A number of observations and comments are directed toward suggesting that more than the usual engineering flavor be given to computer science. The engineering aspect is important because most present difficulties in this field do not involve the theoretical question of whether certain things can be done, bat rather the practical question of how can they be accomplished well and simply. The teaching of computer science could be made more effective by various alterations, for example, the inclusion of a laboratory course in programming, the requirement for a strong minor in something other than mathematics, and more practical coding and less abstract theory, as well as more seriousness and less game playing. Recursive formulas for the numerical evaluation of the real convolution integral are derived for the case in which the impulse response is given analytically. These formulas require considerably less computation time and memory space than the general time series formulas and can be effectively applied for digital simulation of continuous physical systems.

An efficient and numerically stable method is presented for the problem of updating an orthogonal decomposition of a matrix of column (or row) vectors. The fundamental idea is to add a column (or row) analogous to adding an additional row of data in a linear least squares problem. A column (or row) is dropped by a formal scaling with the imaginary unit, √-1, followed by least squares addition of the column (or row). The elimination process for the procedure is successive application of the Givens transformation in modified (more efficient) form. These ideas are illustrated with an implementation of the revised simplex method. The algorithm is a general purpose one that does not account for any particular structure or sparsity in the equations. Some suggested computational tests for determining signs of various controlling parameters in the revised simplex algorithm are mentioned. A simple means of constructing test cases and some sample computing times are presented. [ABSTRACT FROM AUTHOR]

Some social aspects of programming are illuminated through analogies with similar aspects of mathematics and natural languages. The split between pure and applied mathematics is found similarly in programming. The development of natural languages toward flexionless, word-order based language types speaks for programming language design based on general, abstract constructs. By analogy with incidents of the history of artificial, auxiliary languages it is suggested that Fortran and Cobol will remain dominant for a long time to come. The most promising avenues for further work of wide influence are seen to be high quality program literature (i.e. programs) of general utility and studies of questions related to program style. [ABSTRACT FROM AUTHOR]

A description is given of a program for computing the solution to a small number of standard numerical analysis problems to any specified accuracy, up to a limit of 2000 correct decimal places. Each computed number is bounded in an interval with a multiple precision midpoint. Arithmetic operations involving these numbers are executed according to interval arithmetic concepts, with non-significant digits automatically discarded. Details are supplied of problem specification and problem computation. [ABSTRACT FROM AUTHOR]

A fast method is presented for finding a fundamental set of cycles for an undirected finite graph. A spanning tree is grown and the vertices examined in turn, unexamined vertices being stored in a pushdown list to await examination. One stage in the process is to take the top element v of the pushdown list and examine it, i.e. inspect all those edges (v, z) of the graph for which z has not yet been examined. If z is already in the tree, a fundamental cycle is added; if not, the edge (v, z) is placed in the tree. There is exactly one such stage for each of the n vertices of the graph. For large n, the store required increases as n2 and the time as γ where γ depends on the type of graph involved. γ is bounded below by 2 and above by 3, and it is shown thaT both bounds are attained. In terms of storage our algorithm is similar to that of Gotlieb and Corneil and superior to that of Welch; in terms of speed it is similar to that of Welch and superior to that of Gotlieb and Corneil. Tests show our algorithm to be remarkably efficient (γ = 2) on random graphs. [ABSTRACT FROM AUTHOR]

The article reports on several algorithms with their specific computational dynamics. A specific algorithm with its corresponding formula which provides for the procedure for deriving a certain value is provided. The algorithms include, among others, algorithm 290 for linear equations, algorithm 291 for logarithm of gamma functions, and algorithm 178 for direct search. Moreover, the algorithms are written in the ALGOL 60 Reference Language, Standard FORTRAN, and Basic FORTRAN. Specific instructions on how to submit algorithms are also included.

Several letters to the editor are presented in response to articles in the previous issues including "A Comparison of the Primal-Simplex and Primal-Dual Algorithms for Linear Programming," by R.K. Mueller and L. Cooper, "Algorithm and Formula," by T. Wangsness and J. Franklin, and a letter which further expounded the terms algorithm and program.

The elimination procedure as described by Williams has been coded in LISP and FORMAC and used in solving systems of polynomial equations. It is found that the method is very effective in the case of small systems, where it yields all solutions without the need for initial estimates. The method, by itself, appears inappropriate, however, in the solution of large systems of equations due to the explosive growth in the intermediate equations and the hazards which arise when the coefficients are truncated. A comparison is made with difficulties found in other problems in non-numerical mathematics such as symbolic integration and simplification. [ABSTRACT FROM AUTHOR]

Comments on the implementation of researcher E. Minieka's algorithms in computing the k shortest paths between pairs of vertices of a graph. Criticism of Minieka's extended proposition; Comparison of the Minieka algorithm with other algorithms; Reduction of running time in the estimates of paths.

From the inequality 108 < 227, we are likely to conclude that we can represent 8-digit decimal floating-point numbers accurately by 27-bit floating-point numbers. However, we need 28 significant bits to represent some 8-digit numbers accurately. In general, we can show that if 10p < 2q-1, then q significant bits are always enough for p-digit decimal accuracy. Finally, we can define a compact 27-bit floating-point representation that will give 28 significant bits, for numbers of practical importance. [ABSTRACT FROM AUTHOR]

This article presents information on several articles related to computer science. In the article "Application of LISP to Sequence Prediction," by Paul W. Abrahams, a LISP program that analyzes sequences of letters and numbers is described. The program takes as input a sequence such as A C E G I and so on and produces as output the next element of the sequence, in this ease K. The program does this by creating a LISP program that will generate the nth element of the sequence, given n, and then executing this program with the length of the given sequence plus one as argument. In the article "Models for Mathematical Systems," by Alfred H. Morris, a program, written for the IBM 7090, which defines a model for a finite collection of associative algebras for the computer, is described and illustrated. The program contains a structure broad enough in scope to allow one to perform operations on such diverse mathematical concepts as differential equations, infinite series and differential forms in a simple yet comprehensive manner, while also serving in a foundation upon which a variety of higher level symbol manipulation languages can be developed.