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Journal of the ACM (JACM), Volume 14 Issue 1, Jan. 1967

The Synthesis of Algorithmic Systems
Alan J. Perlis
Pages: 1-9
DOI: 10.1145/321371.321372

Sieving Procedures on a Digital Computer
Marvin C. Wunderlich
Pages: 10-19
DOI: 10.1145/321371.321373
Many sequences are most efficiently generated on a digital computer with a sieving procedure in which one represents in the main memory of the machine a set of elements known to contain the desired sequence and then systematically sieves out...

Statistical Discrimination of the Synonymy/Antonymy Relationship Between Words
P. A. W. Lewis, P. B. Baxendale, J. L. Bennett
Pages: 20-44
DOI: 10.1145/321371.321374
A basic hypothesis is stated about the contextual and co-occurrence properties of synonymous words. On the basis of this hypothesis, several statistics are derived for use in discriminating between pairs of words which are synonymous and pairs...

A Computer Program for the Nonnumerical Testing and Reduction of Sets of Algebraic Partial Differential Equations
Carl H. Brans
Pages: 45-62
DOI: 10.1145/321371.321375
A program is described which enables a digital computer to perform the formal algebraic manipulations and differentiations required to test a set of algebraic partial differential equations for consistency, and, if the set is consistent, to...

Computable Error Bounds for Direct Solution of Linear Equations
Bruce A. Chartres, James C. Geuder
Pages: 63-71
DOI: 10.1145/321371.321376
An error analysis of direct methods (i.e., Gaussian elimination or triangular factorization) of solving simultaneous linear algebraic equations is performed in the backward mode, in which the computational errors are expressed as perturbations...

A Modification of Davidon's Minimization Method to Accept Difference Approximations of Derivatives
G. W. Stewart, III
Pages: 72-83
DOI: 10.1145/321371.321377
A modification of Davidon's method for the unconstrained minimization of a function of several variables is proposed in which the gradient vector is approximated by differences. The step sizes for the differencing are calculated from information...

A Multistep Generalization of Runge-Kutta Methods With Four or Five Stages
John C. Butcher
Pages: 84-99
DOI: 10.1145/321371.321378
To obtain high-order integration methods for ordinary differential equatic which combine to some extent the advantage of Runge-Kutta methods on one hand and line multistep methods on the other, the use of “modified multistep” or...

Fourier Analysis of Uniform Random Number Generators
R. R. Coveyou, R. D. Macpherson
Pages: 100-119
DOI: 10.1145/321371.321379
A method of analysis of uniform random number generators is developed, applicable to almost all practical methods of generation. The method is that of Fourier analysis of the output sequences of such generators. With this tool it is possible to...

Binomial-Weighted Orthogonal Polynomials
Tzay Y. Young
Pages: 120-127
DOI: 10.1145/321371.321380
This paper discusses a set of polynomials, {&phgr;r(s)}, orthogonal over a discrete range, with binomial distribution, b(s; n,...

Subresultants and Reduced Polynomial Remainder Sequences
George E. Collins
Pages: 128-142
DOI: 10.1145/321371.321381
Let @@@@ be an integral domain, P(@@@@) the integral domain of polynomials over @@@@. Let P, Q ∈ P(@@@@) with m @@@@ deg (P) ≥ n = deg...

Modified Multistep Methods Based on a Nonpolynomial Interpolant
Brian Shaw
Pages: 143-154
DOI: 10.1145/321371.321382
A new class of multistep formulas with variable coefficients is derived for the numerical integration of the ordinary differential equation y′ = f(x, y) whose theoretical...

Multistep Methods With Modified Predictors and Correctors
J. J. Kohfeld, G. T. Thompson
Pages: 155-166
DOI: 10.1145/321371.321383
In April, 1964, Gragg and Stetter published a set of numerical methods for solving y′ = f(x, y) which rely on some very accurate correctors, using a “nonstep”...

A Remark on Post Normal Systems
Ann Yasuhara
Pages: 167-171
DOI: 10.1145/321371.321384
Let N(T) be the normal system of Post which corresponds to the Thue system, T, as in Martin Davis, Computability and Unsolvability (McGraw-Hill, New York, 1958), pp. 98-100. It...

Stack automata and compiling
Seymour Ginsburg, Sheila A. Greibach, Michael A. Harrison
Pages: 172-201
DOI: 10.1145/321371.321385
Compilation consists of two parts, recognition and translation. A mathematical model is presented which embodies salient features of many modern compiling techniques. The model, called the stack automaton, has the desirable feature of being...