ACM '58最新文献

{"title":"The design of fixed-point iterations","authors":"A. C. Downing","doi":"10.1145/610937.611001","DOIUrl":"https://doi.org/10.1145/610937.611001","url":null,"abstract":"where the residual ~(~) tends to zero as v increases without limit° Such iterations are self-correcting. The ultimate accuracy of ~ will depend upon the rounding errors committed in determining f(~)~(~). These rounding errors may be minimized in a large class of problems by computinE [~kf(~)]~(~)2-k provided one ~nows a priori that If~)I~ ~k The previous iteration always provides a lower bound for k. In this manner it is possible to continue the iteration until the interval of uncertainty of the final ~ is minimal. For second-order iterative procedures in a binary computer with places to the right of the binary point, then one obtains","PeriodicalId":174899,"journal":{"name":"ACM '58","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126985597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Translation between algebraic coding languages","authors":"R. M. Graham","doi":"10.1145/610937.610964","DOIUrl":"https://doi.org/10.1145/610937.610964","url":null,"abstract":"This paper will describe some results of a project to develop a computer program for translating the IT language (Carnegie institute of Technology Internal Translator for the IBM 650) into the FORTRAN language (Automatic Coding System for the IBM 704). The project had a twofold objective, (a) to provide a means by which a checked out program for the IBM 650 may be executed on the IBM 704 without having to recode and recheck the program, and (b) to study the problem of translation from one coding language to another.","PeriodicalId":174899,"journal":{"name":"ACM '58","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131035166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generation of spherical Bessel functions in digital computers","authors":"F. J. Corbató, J. Uretsky","doi":"10.1145/610937.610981","DOIUrl":"https://doi.org/10.1145/610937.610981","url":null,"abstract":"Summar Z When one attempts to solve a problem on a digital computer one often finds it necessary to furnish the machine with a great many values of some well~known analytic functions There are essentially two ways to do thiss One technique is to read the values from a table of function values kept in internal storage during the computations Alternatively~ the values of the function may be generated~ as needed~ by the computers In either cases it is desirable to compute all function values internally~ Extensive use has been made of a function generator in connection with the solutions of the spherical Bessel equation~ It turns out that in the case of these functions it is possible to formulate a method of generation which is particularly well adapted for machine uses The method is based upon the use of recurrence relations which are quite simple in form, thereby being easily coded~ and yet give high numerical accuracy throughout the range of order and argument met in most applications. The use of recurrence relations implies~ of courser that the method would be most efficiently utilized in those calculations where one requires the value of the function for many different orders at each specified value of the argument. The purpose of this paper is to show how the recurrence relations may be used in a straightforward manner for generating in a digital computer the various types of spherical Bessel functions~","PeriodicalId":174899,"journal":{"name":"ACM '58","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125058588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The solution of tall distribution problems","authors":"B. Galler, P. S. Dwyer","doi":"10.1145/610937.610999","DOIUrl":"https://doi.org/10.1145/610937.610999","url":null,"abstract":"The problem is to allocate the shipments (i.eo, to find the numbers xij) so as to minimize T. More formally, the problem is to P q find integers xij such that (1) xij > O, (2) Z xij = a (3) Z x i = bi, i=l J ' j=l and such that T is minimized. In many situations, particularly in industrial and governmental operations, it happens that p is much greater than q (in which case the matrix (cij) is said to be \"tall\"). This would occur, for instance, in csse there were just a few mannfacturing plants which were supplying many warehouses and for ret~il customer~ with their products. On the other hsnd, it might also happen that q is much greater than p (in ~hich csse the cost matrix is said to be \"flat\"). Such a situation would arise in","PeriodicalId":174899,"journal":{"name":"ACM '58","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125296384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A study of numerical methods for solving differential equations","authors":"P. Williams","doi":"10.1145/610937.610941","DOIUrl":"https://doi.org/10.1145/610937.610941","url":null,"abstract":"By far the raajo~~Tty of numae#±cal integration formulas are of the multi-point type~ In these types the unknown point on the integral is found as a function of known previous points and derivatives at those points~ The number of these previous values varies from one to four or fi~eo Using more than that becomes quite ~nwieldyo A refinement of the multi-point formulas is the \"predictor-corrector qt technique° Here a formula such as discussed above (eog.~ one using the previous ordinate and the four previous derivatives) is used to predict the desired point° Then a completely different formula is used to correct this value° This latter formula employs the value of the derivative at the point just predicted° Consequently it serves as a check on the accuracy of the predicted points More specifically~ one of these formulas is used to integrate ahead by extrapo]ation~ and the other is used to check the extrapolated value° The predicted and corrected values are required to agree to within a predetermined tolerance. If this requirement is not met~ then the integration increment can be reduced. Conversely, if the values agree closely enough, then the integration increment m a y b e increased to speed up the solution. Three predictor-corrector type routines were programmed: (i) Adams-Moulton (2) Adams-Bashforth (3) Milne (A fourth multi-point formula was tested and has been used extensively at GEL~C. It employs only a predictor formula using three previous points. It was programmed by G° R. Slayton and is incorporated into his routine, DIDA$, a Digital Differential Analyzer Simulator. Both the accuracy and speed of this program seem to be quite good.) These methods require the knowledge of four starting points on the solution (three in the case of DIDAS) to get started. Various methods exist for finding these values, one of which is the method of Runge-Kutta. Runge-Kutta Method A method was devised by C. Runge and extended by W. Kutta around the turn of this century. This method is almost unique among numerical integration techniques in that it requires only one point to predict the next. This is the one single-point method that competes with the multi-point methods in accuracy.","PeriodicalId":174899,"journal":{"name":"ACM '58","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123034939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Projections, least squares, and constrained minimization problem","authors":"D. Morrison","doi":"10.1145/610937.610985","DOIUrl":"https://doi.org/10.1145/610937.610985","url":null,"abstract":"The notion of a projectlon is important in the solution of a n u m b e r of problems. The m o s t familiar is the least squares prohlern~ but the s a m e ideas appear in different guises in techniques for solving constrained minimization p r o b l e m s {linear and nonlinear p r o g r a m m i n g and C h e b y c h e v fitting problems~ for example). In thxs note w e discuss a m e t h o d f o r numerically finding projections in a finite dimensional vector space. W e will also discuss briefly the connection between projections, least square p r o b l e m s and constrained minimization p r o b l e m s. Given a vector space V of dimension n, a suhspace S of dimension r, and a vector b~V, the projection P b of b onto S has the properties: i) Pb~S, ii) (b-Pb,w) = 0 for all w~S. T h e projection p r o b l e m is to find b = P b for a given subspace S and a given vector b o The subspace S is given by specifying a set of vectors al~ ... a which m span S. W e let A be the matrix w h o s e c o l u m n s are a.. The m e t h o d consists J of finding a rotation matrix R so that the a u g m e n t e d matrix (Ab) is transformed~ via multiplication on the left by R, into an upper triangular matrix a u g m e n t e d by n-(m+i) rows of zeros: (I) R(Ab) m I i T = 0 • i 0 n-(m+l) The integers bordering the matrix indicate the dimensions of the various components. W e a s s u m e for the m o m e n t that the triangular matrix T has no zeros on the diagonal, so that the system T k = C has a solution k. T h e n the m a i n results are","PeriodicalId":174899,"journal":{"name":"ACM '58","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114850830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Machine implementation of symbolic programming","authors":"E. M. Boehm, T. Steel","doi":"10.1145/610937.610953","DOIUrl":"https://doi.org/10.1145/610937.610953","url":null,"abstract":"Apart from mnemonic aids~ the principal featuz~e of symbolic coding is that referents and their relata maintain the same association when intervening elements are altered in number. A price is paid for this freedom as symbolic languages are uninterpretable by machine circuits without aid. A special program is required. The principal disagreeable characteristic of an assembly program is the amount of time it occupies in execution. By attempting to minimize the frequency of reassembly~ the programmer is forced to employ two languages in parallel. Logic shows that the only escape from this dilemma is to place some burden of the assembly on that program~hich loads codes into the machine storage for immediate execution° At once a question arises concerning the propriety of performing even a partial assembly at each machine pass. It is apparent to anyone familiar with historical assembly programs that the major time involved comes not from the internal processing but from the considerable read-in time associated with the usual methods of representing symbolic information. As this information is originally written by a human coder and then reproduced into, say, punched cards, again by a human operator, it is evidently impractical to start the process with binary encoding or some other form of compact expression. It is, however, possible to reduce this original writing to some new form of condensed encoding by computer processing and to use this form exclusively in subsequent operations. With care this can be done and not destroy the desirable features of the original representation. The basic concept in this system is a second encoding schema for the information concerning a program originally described in the symbolic language. This encoding, called the 'squoze encoding, is at variance with the programmers' encoding in several respects. First, it is fundamentally binary, employing only two basic marks, while the progra~ner enjoys the use of fifty. Secondly, the organization of information is quite different in the squoze encoding. All information concerning a particular instruction occurs together in the original expression. This is not the pattern in the squoze encoding. For example, the location symbols associated with the various instructions and storage cells are collected in a single, separate list. This proves to be most desirable for computational purposes when consideration is given to the special role played by such symbols. Finally~ and with perhaps the most significance to the casual observer, the squoze encoding is far more conservative …","PeriodicalId":174899,"journal":{"name":"ACM '58","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121681053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reporting computer performance to management","authors":"J. A. Campise","doi":"10.1145/610937.610989","DOIUrl":"https://doi.org/10.1145/610937.610989","url":null,"abstract":"As we enter the second decade of computing some of the original glamotu ~ and mystery begins to fade. During the past year, the luster has dulled rapidly as management has become increasingly cost conscious. The cost of running a medium or large scale digital computer installation can be a very noticeable figure in an operating cash budget. The problem is not simply to keep management informed of the facts about our computer installations~ We must do this, of course, but we must recognize that the executives of our companies usually need assistance in analysing these facts. The problem is really one of presenting an honest picture while re-establishing justification for our existence with each progress or performance report we submit. The two basic questions which must be answered repeatedly are: (i) How well are we using our machines, (2) How well are the machines performing mechan~ cally? In order to answer these questions we must decide what data to record in our day to day operations, how to record these data, how to classify these data~ and how to present and interpret the results. While it is true that the temperament of management differs widely from company to company~ there are several basic pieces of information which we must collect in order to show that we are paying our way; since in the final analysis~ the ultimate proof that we must all display is that our existence causes a larger increase in the black ink side of the balance sheet than it causes on the red ink side. This extra bookkeeping is like so many of our routine duties-a necessary evil; so let's recognize this and accept it just as we accept taxes, television comnercials, and tranquilizer pills. As a matter of fact, it is probable that every one of us is keeping a log of operations of some sort already. Now it is a matter of getting the right information down on the log and classifying that information so that it can be easily compiled into reports for management. I will tell you how we have approached this problem in our company, in the hope that this will spark Just one idea in your own mind in order that we as a group may keep management aware of the acute need for a well run computing installation no matter what the slope of the economic curve. Let the …","PeriodicalId":174899,"journal":{"name":"ACM '58","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125466830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometrics of spiral bridge design","authors":"J. Belzer","doi":"10.1145/610937.610948","DOIUrl":"https://doi.org/10.1145/610937.610948","url":null,"abstract":"Some of the largest financial outlays in the entire highway construction program are made for the construction of bridges which span railroads, tigers, and other high~aySo In order to fit in wlth the overall design of the highways, these bridges frequently connect roads not in a straight line~ Usually they begin as a straight line following the road, go into a spiral which connects to a circle, and go back into a spiral w:-~ich connects with the road on the other side° As part of the designs the engineers must supply the contractor with detailed specifications including the sizes ana lengths of beams required in the bridge construction. To insure properly fitted parts, accurate measurements are, of courser vitals In the past engineers have used empirically obtained handbook tables to determine these dimensions where spiral bridges are involved° Now, however, automatic digital computers can handle such problems quickly and accurately. To perform this task on digital computers, mathematical representations of the geometric configurations of spiral bridge structures are here developed The spiral represented here is a transition curve between a straight line and a circle and provides a continuous change in curvature from zero to that of a circle° The length of the spiral is usually known, and the equation chosen to represent the spiral satisfying these requirements is a function of its length, and is y \" Ks 3 Equation (i) where s is the distance along the spiral from the origin to any point on the spiral, and K is a constant to be determined.","PeriodicalId":174899,"journal":{"name":"ACM '58","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124814718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An analysis of carry transmission in computer addition","authors":"Sullivan G. Campbell, G. H. Rosser","doi":"10.1145/610937.610962","DOIUrl":"https://doi.org/10.1145/610937.610962","url":null,"abstract":"Since all arithmetic operations reduce ultimately to addition, a basic consideration in designing a high speed computing automation is fast addition; and a basic difficulty in achieving fast addition is the carry problem, inasmuch as a single carry may propagate through an entire addition. Further, the expected number of carries from the addition of words of equivalent information is greatest in the binary number system, which is commonly used in the high speed scientific computer because of high storage efficiency and easy mechanization. Nor is the problem avoided altogether by going to a decimal radix: for a binary coded decimal or biquinary representation is usually used, and the binary problem still exists in altered form. It is the purpose of this paper to determine the effect of various methods of increasing the speed of binary addition by \"carry sensing\", designed to increase the speed with which carries are propagated. Any procedure which alters the expected length of a carry will be called a \"carry transformation\" T; by T:c i --~ cj, we mean a carry transformation T which transforms a carry of i places into a carry of j places. Assuming that we are dealing with words of n bits (binary digits), the longest possible carry is n places; then T:c n-~ c k means that the longest possible carry in the equivalent transformed system is k places. By determining the various possible carry transformations T, we can accomplish several objectives., Perhaps most important, any information we possess about the binary system (which is the easiest number system to deal with) is automatically transformed into equivalent information about the transformed system. Further, it may be desirable to use more than one kind of transformation on the same circuit, or to determine what succession of transformations is most efficient under a given set of rules. Finally, any number system used may be regarded simply as a transformed binary system so that information about the binary system only is necessary to solve carry problems in any radix. (The basic information required includes the longest expected carry as a function of the number of digits used, and the probabilities Pm that the longest carry does not exceed m places; these probabilities may be calculated recursively as a function of m and n, but the computation is difficult even in the","PeriodicalId":174899,"journal":{"name":"ACM '58","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122509155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}