Mario L. Juncosa

Some numerical experiments using Newton's method for nonlinear parabolic and elliptic boundary-value problems

Using a generalization of Newtons method, a non-linear parabolic equation of the form <italic>u<subscrpt>t</subscrpt></italic> - <italic>u<subscrpt>xx</subscrpt></italic> = <italic>g</italic>(<italic>u</italic>), and a non-linear elliptic equation <italic>u<subscrpt>xx</subscrpt></italic> + <italic>u<subscrpt>yy</subscrpt></italic> = <italic>e<supscrpt>u</supscrpt></italic>, are solved numerically. Comparison of these results with results obtained using the Picard iteration procedure show that in many cases the quasilinearization method offers substantial advantages in both time and accuracy.

Cutting Some Trees to See the Forest: On Aggregation and Disaggregation in Combat Models

Most models of air and land combat use schemes of aggregation and disaggregation in representing combat systems, in spatial configuration, and in depicting progress of a battle. For example, the use of firepower «scores» is an extreme case of aggregation of weapons into a single measure. Combining like systems into weapons categories, partial aggregation, is a common approach to representing a large number of aircraft or ground weapons types. This article explores different approaches to aggregation and what is known theoretically about aggregation and disaggregation in combat models of the Lanchester type commonly called «square law» in two dimensions. It defines requirements for consistency between aggregate and higher-dimensioned models of this type. Some important conclusions are that aggregation should take into account the specific capabilities of the opponent (raising concern about many «scored» approaches which attempt to evaluate force components in isolation), and that partial aggregation (grouping «like» systems) and disaggregation of previously aggregated results can only be done consistently when certain restrictions on the relative attrition capabilities of weapons systems hold. When this is the case, specific weightings for the force resources can be determined for the partial aggregations

On the Increase of Convergence Rates of Relaxation Procedures for Elliptic Partial Difference Equations

Occasionally in the numerical solution of elliptic partial differential equations the rate of convergence of relaxation methods to the solution is adversely affected by the relative proximity of certain points in the grid. It has been proposed that the removal of the unknown functional values at these points by Gaussian elimination may accelerate the convergence. By application of the Perron-Frobenius theory of non-negative matrices it is shown that the rates of convergence of the Jacobi-Richardson and Gauss-Seidel iterations are not decreased and could be increased by this elimination. Although this may indicate that the elimination could improve the convergence rate for overrelaxation, it is still strictly an unsolved problem.

ACM Publication Policies and Plans

was mainly due to his efforts that the ACM Journal was established as an important contribution to the growth of computer technology. It was under his direction that the Journal grew impressively in size and, more importantly, in the quality of the technical papers. With former ACM President, Dr. John W. C a r l and others, Dr. Alt gave impetus to the establishment of the Communications in recognition of the need to have timely information given to ACM members on important topics more qmckly than is possible in the Journal. Dr. Alt has made an important contribution to the computing field; ACM members and computing people everywhere owe him a real debt of gratitude. Many have asked about the objectives of the Journal and the Communzca-tions, and the similarities and differences of these two publications. The Journal will generally accept papers of a research nature, papers marking significant advances in computer technology and papers which are less temporal in nature and more generally applicable as reports of research and developments to the computing field. The Communications is designed to bnng to the attention of ACM members information in the computing field of a more immediate or current nature. More precisely, it will contain preliminary reports of research m progress, information on computer standards, news and notices, and articles on techniques and applications. The establishment of the Communwat,ons pays tribute to the fact that the computing field is young and growing rapidly and that much information of a current and immediate nature should be made available to ACM members on a monthly basis. Certainly there will be some overlap in the kinds of papers appearing in these two publications. Neither publication will purposely emphasize certain kinds of articles. For example, papers on programming research and development will appear in both the Journal and the Communicatwns depending on the particular orientation of the paper. In general, the publications will accept papers on computer methods, applications and design. Every effort will be made to continue and hasten the trend toward a better balance of papers. Probably because numerical analysis is so closely identified with the well disciplined field of mathematics, there has been a preponderance of papers in that field. Every effort will be made in the future to publish good papers on computer programming and business applications. In addition, of course, papers on computer logic, system design, and hardware will 121

Our nuclear future: an era of clean energy abundance

This analysis develops and predicts a politically controversial idea, namely that nuclear fission power will be the dominant energy resource of the 21st century. Abundant energy enables higher and more efficient utilization of resources. Energy drives the engines of industrial and food production, transportation, building construction, space heating, transformation of landscapes, recreation, etc. This article compares other energy alternatives with the potential of nuclear fission power. It predicts that several hundred nuclear plants, each nominally of 10 gigawatts capacity, could supply the world’s energy requirements without creation of polluting greenhouse gases. Moreover, the superabundance of power this would represent could feed the world, supply its drinking water, and raise the per capita income and standard of living to levels where total human population would level off at an acceptable number. However, realization of such benefits requires unprecedented world cooperation, and these issues are ...

Invariant imbedding and the solution of Fredholm integral equations with displacement Kernels— comparative numerical experiments

This paper compares the relative efficiencies of the invariant imbedding method with the traditional solution techniques of successive approximations (Picard method), linear algebraic equations, and Sokolovs method of averaging functional corrections in solving numerically two representatives of a class of Fredholm integral equations. The criterion of efficiency is the amount of computing time necessary to obtain the solution to a specified degree of accuracy. The results of this computational investigation indicate that invariant imbedding has definite numerical advantages; more information was obtained in the same length of time as with the other methods, or even in less time. The conclusion emphasized is that a routine application of invariant imbedding may be expected to be computationally competitive with, if not superior to, a routine application of other methods for the solution of some classes of Fredholm integral equations.

Optimal utilization and extension of interoffice trunking facilities

Many optimization problems in the communications field are characterized by the fact that they involve large numbers of highly interconnected variables. This has forced communications engineers, planners, and managers to resort to various suboptimization schemes, many of which have been of the empirical or trial-and-error types. This situation has in large part been caused by the lack of adequate mathematical and numerical techniques for analyzing and solving such problems.

Transitions 1959--1964

The years 1959–1964, when I served for three years as editor-in-chief of the J urnal of the Association for Computing Machinery and then three as chairman of the editorial board, were years of rather substantial transition for the computer and computing fields, the ACM, and its publications at that time. Prior to this time, a very diverse population of electrical engineers, mathematicians, logicians, statisticians, physicists, other scientists, business people, and others all made contributions to the design and construction of computers, to their applications, and relevant theoretical bases. Even though not an insignificant number of individuals of different professions in the population may not have even been able to understand each other, the “computing machinery” was what was common to all; hence, the name of the association. The diversity of subjects, broad spectrum of abstractness, variable depth, and quality of papers presented and/or published in various publications, including those of the ACM, were far greater than most proceedings of conferences and journals of specific scientific, technological, medical, and other professions. Nevertheless, toward the end of the decade of the 1950s, as the analog computer was becoming scarcely a memory in the computing world as a whole and transition from vacuum tube, cathode tube, and ferrite core to memories based on transistors was essentially complete, some more broadly thinking people began to feel that there was something more than just knowledge about computers or computing that was emerging from this miscellany. Indeed, what it was was the gestation and birth of new science, the computer and information sciences, which included communications, with very wide and very important applications and the ACM was the society for it. It had all the attributes of a science; it had a body of knowledge and it had theories that had predictive power, verifiable by experience, and alterable when new knowledge or experience required it (not different in these respects from physics and chemistry, sciences with their theories and vast applications). Indeed, in the very early 1960s, it was proposed that the society change its name to the Association for the Computing and Information Sciences, ACIS for short, easy to remember, pronounce, and truly would announce that it was a science that the association represented. There were very many verbal exchanges of strong opinion on the proposal, two featured pro and con pieces in the Communications of the ACM, and a few other opinions put down in print. One that I recall was by Bernie Galler of the University of Michigan clearly stating his reasons, similar to the above, why Computer Science was indeed a science. Some arguments against change were that the society had already established itself in a decade under its current name and some people may not recognize that it was the same society under a new name (in spite of the fact that in that very year of the debate 20% of the NYSE-listed companies changed their name, a few to initials or acronyms of their former full names). Other opponents to change of name did not consider their activities or profession as science; they were happy with the association as