July 1969 - Vol. 12 No. 7

July 1969 issue cover image

Features

Research and Advances

Polynomial and spline approximation by quadratic programming

The problem of approximation to a given function, or of fitting a given set of data, where the approximating function is required to have certain of its derivatives of specified sign over the whole range of approximation, is studied. Two approaches are presented, in each of which quadratic programming is used to provide both the constraints on the derivatives and the selection of the function which yields the best fit. The first is a modified Berstein polynomial scheme, and the second is a spline fit.
Research and Advances

Generating pseudorandom numbers on a two’s complement machine such as the IBM 360

The familiar multiplicative congruential generator is examined in the context of the type of two's complement arithmetic used in the IBM 360 series. Different sequences of residues are considered and relationships established among them. It is shown that a sequence of positive and negative residues may be produced more simply and econimically than with the conventional approach and yet have twice the period of the latter without loss of desirable statistical properties. Another easily generated sequence involving absolute values is also shown to have twice the period but with the less attractive statistical properties. The statistical properties of these sequences are given and related to previously established criteria.
Research and Advances

Automatic contour map

Some methods for contour mapping by means of a digital plotter are dicussed, and a new method is presented that is simple enough to be implemented by programs with a rather small number of instructions (about 120 FORTRAN IV instructions are required). Comparisons with some methods proposed by other authors are also performed. A FORTRAN IV program implementing the proposed method is availabel at the Istituto di Elettrotecnica ed Elettronica, Politecnico di Milano.
Research and Advances

Block structures, indirect addressing, and garbage collection

Programming languages have included explicit or implicit block structures to provide a naming convenience for the programmer. However, when indirect addressing is used, as in SNOBOL, naming constraints may be introduced. Two modifications to SNOBOL are described, resulting in two desirable consequences: (1) naming constraints disappear even when there is indirect addressing within function definitions; and (2) there is a significant saving in the number of calls to the garbage collector, because some garbage is collected, at little expense, each time a function returns to its calling program. These modifications have been implemented as an extension to a SNOBOL dialect.

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