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The paper describes a scheme for symbolic manipulation of index expressions which arise as a by-product of the symbolic manipulation of expressions in the matrix calculi described by the authors in a previous paper. This scheme attempts program optimization by transforming the original algorithm rather than the machine code. The goal is to automatically generate code for handling the tedious address calculations necessitated by complicated data structures. The paper is therefore preoccupied with "indexing by position." The relationship of "indexing by name" and "indexing by position" is discussed. [ABSTRACT FROM AUTHOR]

The article presents several research papers relating to algorithms. The paper "Greatest Common Divisor of n Integers and Multipliers" presents an algorithm which calculates the greatest common divisor, IGCD, of n integers. Details of the method and comparisons to other algorithms are also given. The algorithm is a new version of the Euclidean algorithm for n integers. The n-1 calculations of the greatest common divisor of two integers is accomplished by means of a modified version of the Blankinship algorithm. The paper "Exponential Integral Ei (x)" presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract NAS7-100, sponsored by the National Aeronautics and Space Administration. It presents an algorithm which was compiled and executed without any modification on a UNIVAC 1108 computer. An unfortunate precedent has been set in several recent algorithms of using an illegal FORTRAN construction.

Given the horizontal and vertical projections of a finite binary pattern f, can we reconstruct the original pattern f? In this paper we give a characterization of patterns that ore reconstructable from their projections. Three algorithms ore developed to reconstruct both unambiguous and ambiguous patterns, it is shown that an unambiguous pattern can be perfectly reconstructed in time m × n and that a pattern similar to an ambiguous pattern can also be constructed in time m × n, where m, n are the dimensions of the pattern frame. [ABSTRACT FROM AUTHOR]

This paper is concerned with a review and examination of several existing algorithms for the zero-one programming problem. Computational experience is summarized. The machine time and storage requirements of several of the algorithms are compared over several test problems of small and intermediate size. Computer experiments still provide little hope of solving problems with over 100 variables with a reasonable amount of machine time. [ABSTRACT FROM AUTHOR]

The article presents information on the publication of a book "Applied Statistics, Algorithms," relevant to statistics, by the Royal Statistical Society in cooperation with the Science Research Council's Working Party on Statistical Computing. A policy statement describing the editorial policy appears in "Applied Statistics," Vol. 1. No. 1 (1968). A support paper describing the expected contents of the external specification and making recommendation for the layout of algorithms and for programming strategy will appear in the following issue.

The QR iteration for the eigenvalues of a symmetric tridiagonal matrix can be accelerated by incorporating a sequence of origin shifts. The origin shift may be either subtracted directly from the diagonal elements of the matrix or incorporated by means of an implicit algorithm. Both methods have drawbacks: the direct method can unnecessarily degrade small eigen-values, while the implicit method can effectively loose the shift and thereby retard the convergence. This paper presents a new method which has neither drawback. [ABSTRACT FROM AUTHOR]

The article discusses the computation of rational approximations using existing algorithms. In a recent paper it is shown that minimax logarithmic approximations are optimal for square root calculations, making the minimax logarithmic problem of practical interest. The authors point out how rational approximations which are best with respect to maximum logarithmic error can be computed by existing algorithms. Suppose one wishes to approximate a positive continuous function "f" by a positive rational function R, then the logarithmic error at a point x is log (f(x))-- log (R(x)). The approximation problem is thus equivalent to ordinary approximation of continuous function g = log (f) by log {R).

The article focuses on a paper indicating the error of algorithmic language ALGOL 60 pointed up by the Algorithm 355 construct in the October 1969 issue of the periodical "Communications of the Automation for Computing Machinery." The procedure statement "p" occurs in the body of this procedure, showing "p" to be a procedure without parameters. As originally submitted, the algorithm contained several procedure statements in which p was replaced by a procedure statement. It is possible that the authors of ALGOL 60 intended to permit this but they did not do so. The author's original form may have been more in the sprit of the ALGOL 60 report but the published form confirms to the syntax of ALGOL 60 as described in the report.