The following paper presents an analysis of algorithms for De Bruijn sequences. It is unusual in that the analysis is carried out empirically rather than analytically.

Given the simple fact that mathematics forms the foundation of computing, mathematics must play a meaningful role in the computer science program. This meaningful role, however, must be substantially less, in content, than a second major. We must avoid the extreme of little or no mathematics in the curriculum. We must, at the same time, avoid the excess of too much mathematics.

Fortran is 21 years old; many would say that it has not reached adulthood but senility. Yet it remains the language of use in the overwhelming majority of scientific applications of computers and no end to this situation is in sight. Moreover, its evolution through the standards process is very slow, too slow to give any hope that Fortran will ever in this way become a language in which structured programs can be easily and effectively written.

article Free Access Share on On Economization of Rational Functions Author: Anthony Ralston Stevens Institute of Technology, Hoboken, New Jersey Stevens Institute of Technology, Hoboken, New JerseyView Profile Authors Info & Claims Journal of the ACMVolume 10Issue 3July 1963 pp 278–282https://doi.org/10.1145/321172.321174Published:01 July 1963Publication History 5citation332DownloadsMetricsTotal Citations5Total Downloads332Last 12 Months6Last 6 weeks3 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

This paper is mainly concerned with three matters relating to predictor-corrector methods. The first is a consideration of the replacement of classical predictors by direct extrapolation, smoothed and unsmoothed, of the first derivative. The second matter discussed is the computational aspects of not iterating the corrector to convergence and the possible use of a convergence factor to test the corrector convergence. Finally, the desirability of using higher order processes as opposed to modifying the results of lower order processes is considered. Some numerical results are given to illustrate the topics discussed. This paper is based on one that was presented at the July 1960 Conference of the British Computer Society in Harrogate.

A class of quadrature formulas is derived which achieve higher accuracy in composite rules (i.e., where the interval of integration is broken up into a number of subintervals) than analogous Newton-Cotes or Gaussian formulas. The cost of this higher accuracy is the computation of one or two more ordinates over the whole interval of integration. The high accuracy is obtained by using Gaussian techniques in the interior of each subinterval and by using the endpoints of each subinterval as abscissas with weights of equal magnitude and opposite sign. In this way when the subintervals are put together only the endpoints of the whole interval of integration remain. It is proved that the abscissas are all real and interior to the subinterval and that the weights corresponding to the interior abscissas are positive. Since the abscissas are not equally spaced, the method is not suited to tabular functions but rather to analytically given functions. The roundoff properties of the formulas are discussed and are shown to be quite good.