# Communications of the ACM

#### Note on stochastic matrices

A formula for numerical integration is prepared, which involves an exponential term. This formula is compared to two standard integration methods, and it is shown that for a large class of differential equations, the exponential …

#### Pei matrix eigenvectors

M. L. Pei [Comm. ACM 5, 10 (Oct. 1962)] gave an explicit inverse for a matrix of the form M + &dgr;I, where M is an n-square matrix of ones and &dgr; is a nonzero parameter. The eigenvalues of the Pei matrix were given by W. S. LaSor …

#### Closing out a print tape

Some computer operating systems have a bad habit of inserting tape marks into the output stream willy-nilly. This often results in loss of output when a tape is scratched after its first file has been printed. Other operating …

#### A semi-iterative process for evaluating arctangents

The technique of obtaining arctangents by inverse interpolation [1] is a relatively long process not suitable for a subroutine. The Taylor series expansion for arguments less than unity converges rather slowly for those near&pgr; …

#### Symmetric list processor

A list processing system in which each list cell contains both a forward and a backward link as well as a datum is described. This system is intended for imbedding in higher level languages capable of calling functions and subroutines …

#### MIRFAC: a compiler based on standard mathematical notation and plain English

A pilot version of the compiler MIRFAC, now in the operation, is described. The chief features of the system, which is intended for the solution of scientific problems, are the presentation of mathematical formulas entirely in …

#### Computer-drawn flowcharts

To meet the need for improved documentation of written computer programs, a simple system for effective communication is presented, which has shown great promise. The programmer describes his program in a simple format, and the …

#### On the approximate solution of Δ u=F(u)

Three-dimensional Dirichlet problems for &Dgr;u = F(u), Fu ≧ 0, are treated numerically by an exceptionally fast, exceptionally accurate numerical method. Programming details, numerous examples and mathematical theory are supplied …

#### A general program for the analysis of square and rectanglar lattice designs

This paper describes a general-purpose program that will handle those incomplete block designs known as square and rectangular lattices. Flow diagrams are given so that the method of calculation may be programmed for any digital …

#### Group participation computer demonstration

Engelbart1 has reported on some demonstrations in which a group functions as various parts of a digital computer. These demonstrations are concerned with binary operations including addition. However, there are occasions when …