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The article offers information on a mathematical procedure for constrained optimization. The program aims to identify the maximum of a multivariable, nonlinear function subject to constraints based on the sequential search method of M.J. Box. It has three subroutines such as JCONSX, JCEK1, and JCENT and user supplied subroutines which include JFUNC and JCNTS1. The subroutine argument lists provide the presentation of the communication between the main program and subroutines. A test is conducted to examine the program through various functions computed on a CDC 6400 computer. The search technique process is discussed.

The article discusses algorithm 446 with regard to ten subroutines for the manipulation of Chebyshev series. The operations performed in the article are the construction of the Chebyshev approximation of functions, the evaluation of the series or their derivative, the integration or differentiation and the construction of negative or fractional powers of such a series. The subroutines are written in ANSI Fortran. They have been used without modification on such computers as the IBM-7094, IBM-360/93 and Univac 1108. The ten subroutines are considered as a single set, principally because they all use the same storage philosophy. All information is transmitted through the CALL-sequence rather than through the use of COMMON statements. Therefore, the user must provide storage for all the series in his main program, taking into account that all operations are performed in double precision. The coefficients of each series occupy a one-dimensional double-precision array according to the rules of ANSI Fortran. When several Chebyshev series are being manipulated, it is convenient to store all the series in a matrix.

The article presents the algorithm HIDE, for the Hidden-Line Plotting Program. HIDE produces a two-dimensional representation of a surface or figure by plotting segments of a succession of curves and each curve is plotted where it is not hidden by any of the curves previously plotted. Explicit provisions are not made in HIDE for perspective plots or for rotations. If. however, the arrays to be plotted are properly transformed before HIDE is called, such effects can be achieved. Developed on Tracor Computing Corp.'s (TCC) UNIVAC 1108 system, HIDE calls several basic systems plotting routines. In the listing, these calls are preceded by comment cards with asterisks across the lines. If HIDE were to be used on a different computer system, calls could be substituted to the corresponding routines of that system, or, if more flexibility were desired, to user-supplied routines. Although partially explained in comment cards, the calling sequences of systems routines called by HIDE will be described more fully here. On TCC's system, these routines write pen codes on magnetic tapes, which are used to drive offline drum plotters.

The article focuses on the use of subroutines in differential equations. Subroutine integrates a set of up to N ordinary differential equations one step of length H, where H may be specified by the user, but is controlled by the subroutine to control the estimated error within a specified tolerance. A multistep predictor corrector method is used whose order is automatically chosen by the subroutine as the integration proceeds. Either an Adams' method or methods suitable for stiff equations can be selected. The starting procedure is automatic and the information retained by the program about previous steps is stored in such a way as to make the interpolation to a nonmesh point straightforward. The programs may call on up to three subroutines. They are DIFFUN, PEDERV and MATINV. The first, DIFFUN, must be provided always, and it must evaluate the derivatives of the dependent variables Y with respect to the independent variable T and place the results in DY. MATINV must be provided if stiff methods are requested. It should invert the matrix PW which is of size N by N. PERDERV is another optional subroutine called only if the method flag MF is set to 1.

Describes a universal two-dimensional data plotting software system, called AMESPLOT, whose syntax is based on the ordering of subroutine modules. Outline of the elements common to all types of data plots; Key features of data plotting; Structuring of plots from multiple, independent, self-contained subplots; Utility software of AMESPLOT.

Describes a combination hardware/software monitor, called INT, designed to control a wide variety of real-time input/output (I/O) devices. Primary function of hardware and software; Set of meta-instructions which consists mostly of machine-language subroutine calls; Implementation of the monitor on a small general-purpose machine.

Describes how a series of four problems of increasing difficulty were solved using a set of subroutines created to allow algebraic manipulations on the IBM 7094 computer. Representation of algebraic expressions; Notation and memory organization; Descriptions of routines which were developed for algebraic manipulation.

Discusses matrix computations using Fortran computer program language and paging. Influence of the order of nested loops on the efficiency of conventional Fortran programs; Effect of nested loop modifications on large programs run under paging-based operating system.

A computer design is described which permits subroutines to be executed backward as well as forward, either with their instructions unchanged or replaced with conjugate instructions. It is shown that using this concept a number of new subroutine types can be developed with rather unusual properties. Since these properties are analogous to certain matrix operations, a parallel nomenclature is suggested for their classification. [ABSTRACT FROM AUTHOR]

Describes the development of a routine which computes and prints out the symbolic derivative of an absolutely continuous elementary function of one or several variables. List processing; Chain rule; Subroutines; Recursion.

Discusses the use of proper COBOL coding techniques to write FORTRAN IV subroutines that may be called from COBOL main programs. Accounting for differences in storage allocation and library routines between the two languages; Enabling of the programmer to take advantage of the most useful properties of each language while minimizing their respective disadvantages.

Analyzes certain nonrandom properties of a commonly used random number generator. Warning against indiscriminate application of random number generators; Four triple-precision (132-bit) floating point arithmetic subroutines; Control Data 3600 computer version of the subroutines.

The article offers information on a mathematical procedure for Bromwich's integral (BROMIN) using Gaussian quadrature formulas. BROMIN computes the abscissas and weights of the quadrature formula following the conditions on the value of c, s, and the F(x). It does not recognize the use of complex arithmetic due to the conflict it may have to the conversion to a double precision subroutine. The relative errors in the abscissas posted larger figures compared with the errors in the weight. A table of the maximum relative errors in abscissas and weights are provided.

The article offers information on a mathematical method that can be used to identify the local minimum function of n variable for an unconstrained problem using Rosenbrock's Function Minimization. Cycle searches similar to each of the n orthogonal unit is a potential method in identifying the local minimum function leading to the generation of a set of n orthogonal unit vectors. These new unit vectors is calculated using the Gram-Schmidt orthogonalization. Users are advised to supply additional subroutines such as FUNCT and MONITOR. Definitions of the parameters used in the program as well as an overview of the routine are provided.

The article focuses on the work of researcher H.L. Morgan related to a new form of interrupt which he proposes to use to control the execution of a program, in his case a file management system called data processing language. Simply stated, he has attached to every subroutine a Boolean expression which, if true, would cause that subroutine to be executed. Since his implementation is via software, a relatively time-consuming check must be made whenever some condition in the program changes. The implementation is described in terms of an IBM 360 environment, but is certainly not limited to it. Essentially the implementation involves the addition of a small associate memory to the CPU which is 12N bytes long. Each entry is 12 bytes wide, and the number of entries is up to the designer of the computer. The utility of this small associative memory is shown under a wide selection of applications. It is by no means definitive in its description. Its only goal is to show the desirability of implementing such a check at the hardware level.

It is shown how Wengert's procedure for computation of derivatives can be implemented conveniently by use of compiler-generated complex addition, subtraction, and linkage to complex arithmetic subroutines, Evaluation of a function and derivative proceed in parallel, as in Wengert's procedure, but with the "imaginary" parts of variables declared complex bearing the values of the derivatives of the real pads. This technique provides a simple way to compute the derivatives of a function, without the need for deriving and programming the evaluation of explicit formulas for the derivatives. [ABSTRACT FROM AUTHOR]

Describes some FORTRAN subroutines to facilitate handling of tape files. Symbolic naming of information files; Tape manipulation.

A letter to the editor is presented discussing the subroutines in Fortran programs.

The article focuses on a subroutine assembly system used on the Feranti Pegasus computer, which requires only one pass and does not maintain a table of information about the subroutine library. All information about and requests for subroutines are contained in special words, called tags, which are recognized by the input routine. Basically there are four types of tags; two types are used by the master program and two types are used by the subroutines themselves, corresponding to calls for cues, calls for parameters, parameter list titles and cue list titles. A list title gives the address of the list, the number of entries in the list, the number of the subordinate and an indication of the type of tag. When the program is read the tags are stored in the high-numbered locations of the store, away from the program itself. When the end pf the master program is reached Assembly scans the tags so far stored and makes a list of index words, one for each subroutine requested and the type of tags that have occurred. At this stage only cue calls and parameters list titles are possible.