ACM '59最新文献

{"title":"Quasi-tridiagonal matrices and type-insensitive difference equations","authors":"S. Schechter","doi":"10.1145/612201.612239","DOIUrl":"https://doi.org/10.1145/612201.612239","url":null,"abstract":"Various discretizations of boundary problems lead to such matrices. That this is so for Poisson's and the biharmonic equations is well known, and has been shown by 0. Karlqvist, A. F. Cornook and others. These authors prcpose the use of @irect, rather than iterative, methods to solve oroblems for these equations° Their methods are extended here to the general matrix (i.I) and it is shown that the positive symmetric difference systems of K. O. Friedrichs also fall into this c!ass~ These inc!ude~ in addition to pure elllptio","PeriodicalId":109454,"journal":{"name":"ACM '59","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1959-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125862506","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":"Generalization of learning in a machine","authors":"R. J. Lee","doi":"10.1145/612201.612227","DOIUrl":"https://doi.org/10.1145/612201.612227","url":null,"abstract":"A small mobile vehicle (~tlggestive of an insect) that can wander about in a suitable environment, directed by the cortex models will illustrate the system concept in simple terms° The vehicle will feed inforzation into the cortex via two photoelectric ~eyes, ~ a microphone 'Sear '~ sensitive to several audio bands, and t~o ~feelers '~ that point forward and to the sides. Its ~atputs will be to turn left, turn rights or head forward° The environment ~ill contain a battery charger~ vari~ ous obstacle configurations, and patterns of sound and light.","PeriodicalId":109454,"journal":{"name":"ACM '59","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1959-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126159059","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 non-linear estimation program","authors":"T. I. Peterson","doi":"10.1145/612201.612287","DOIUrl":"https://doi.org/10.1145/612201.612287","url":null,"abstract":"A program for non-linear estimation has been written for the IBM 704, based on metholology developed by G. E. P. Box, Director of the Statistical Techniques Research Group, Department of Mathematics, Princeton University. The program represents a cooperative effort between that group and the Mathematics and Applications Department, Data Processing Division, IBM.","PeriodicalId":109454,"journal":{"name":"ACM '59","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1959-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123306669","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":"Floating point error analysis","authors":"R. Nickerson","doi":"10.1145/612201.612262","DOIUrl":"https://doi.org/10.1145/612201.612262","url":null,"abstract":"In many floating point calculations it is important to arrange the sequence of calculations such that significant digits are not deleted by intermediate rounding of the numbers. The danger that gross errors may be introduced is always present in floating point calculations, since the number of digits carried in each number is restricted in normal operation by the design of the computer. Although the phenomenon considered here is well-known to people working with numbers, the purpose of this discussion is to provide a direct approach to the examination of calculations in which gross error may be introduced. A pitfall to be avoided is the fact that expanded versions of an expression frequently appear desirable on the surface due to cancellation of terms in the expansion.The problem is illustrated simply by the product of two differences of almost equal error-free integers. All numbers will be restricted to five digits, and numbers having surplus digits will be rounded to five digits.The direct approach yieldsx = (65432-65321) (54321-54304) = (11) (17) = 187. (1)The expanded product approach yieldsx = (65432) (54321) - (65432) (54304) - (65321) (54321) + (65321)(54304) (2)x = (3.5543 - 3.5532 - 3.5483 + 3.5472) x 109 = 0.0 (3)This result is worthless. The restriction of each number to five digits has prevented us from obtaining the correct result by the expanded form. With the aid of a simple notation, we shall show further on that the same situation prevails if the input numbers are not necessarily accurate to N digits.Normalized floating point numbers have their left-most non-zero digit residing at the immediate right of the decimal point. If leading zeros exist between the decimal point and the non-zero digits of the number, the number is termed unnormalized. Floating point operation is characterized by the automatic re-scaling of unnormalized numbers to put them in normalized form. Physically, the process is accomplished by left shifting all of the digits until the leading zeros have been completely removed into the scale factor.More than one leading zero can only be introduced by a summation process. If the sum of a set of numbers has L leading zeros, each term of the sum has up to L implicit leading zeros, and the largest has exactly L implicit leading zeros. The multiplication of two numbers, having L1 and L2 implicit leading zeros each, gives a product containing (L1+L2) implicit leading zeros. The accuracy of calculations leading to a sum of numbers is determined from the number of implicit leading zeros, L, and the total number of digits, N, carried in the calculation. If L > N, as in the above example, the result is meaningless. Calculation procedures which involve summation should thus be examined carefully to establish that an adequate number of digits is retained in the intermediate numbers to obtain the available accuracy in the result. Procedures which produce the normalized result directly are to be preferred, since the intermediate","PeriodicalId":109454,"journal":{"name":"ACM '59","volume":"175 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1959-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115185272","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":"Detached shock problem and related topics","authors":"H. Lieberstein","doi":"10.1145/612201.612279","DOIUrl":"https://doi.org/10.1145/612201.612279","url":null,"abstract":"A finite difference method for solving the Cauchy or initial value problem for elliptic partial differential equations as introduced in (1) and further developed in (2) will be the principal topic discussed here. Involved in this discussion, also, will be certain basic notions related to the (analytic) stability of such problems as developed in (2) and (3). Contributions to the theory of hypersonic flow which resulted from application of this numerical method to the inviscid portion of the flow in the nose region of a blunt nosed body (1) (2) (4) and, also, a successful attack on the related boundary layer problem using a modified Crank-Nicolson technique (5) will be described. It will be shown further that the numerical method given in (2) is useful in resolving certain scientific questions in connection with engineering design of Pierce type electron guns.","PeriodicalId":109454,"journal":{"name":"ACM '59","volume":"120 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1959-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116582930","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 machine loading problem","authors":"Kurt Eisemann, Janice R. Lourie","doi":"10.1145/612201.612235","DOIUrl":"https://doi.org/10.1145/612201.612235","url":null,"abstract":"The Machine Loading Problem is a special case of the general Linear Programming Problem and may be described mathematically as follows: Subject to the following constraints all x. @ 0 ij find values X;{ which minimize the functionZE where, for th~specific problem of the opti~ll ~ cijxij' allocatlon of products to machines, m = number of available machine types n ~ number of distinct products M.. total production time available on machine i I (during a basic time period) P.. total production requirement for product j aij_-amount of time required to produce one unit of product j on machine i bij. 1 in this particular application ci~=~ cost of producing one unit of product j on machine i xi~=j amount of product j to be produced on machine i 28-1-2o Origin of the Geometric Patterns in the Machine Loading Problem The mathematical form of the ~achine l~ading Problem differs from that of the Transportation problem only t~rough the presence of coefficients aij which are not all = io This minor generalization has a drastic effect: given a '~basis'~ m~eo~ a distribution~ in table forms let us draw all possible horizontal and vertical lines interconnecting basis elements~ No longer (as was the case in the Trans~ portation Problem) do we obtain a connected branched chain (topolo~-ically~ a \"tree\"), but rather a number of disconnected pieces~ each piece consisting of a closed loop (or an entry in the special \"slack\" column) with attached branched side-chains (trees)° A simple case is illustrated in Figure i (see next page)° From the point of View of the full Linear Programming matrix of coefficients, this corresponds to the following mathematical equivalent: a set of linearly independent basis vectors is expressed iu terms of auxiliary vectors~ ~ich themselves are no longer independent but are now linearly dependent° it then becomes necessary to solve simultaneous sets of equations dbr~ ing each iteration. As a consequence of the radically altered topo!o-gy, existing programs for the Transportation Problem cannot be simply adapted to the more general Machine Losding version. A new approach was required for the present program, which, during the process of solution, guides the 704 to detect and trace all loops and trees in systematic fashion. Introduction of a new and removal of an existing basis elements which occurs in each iteration of the algorithm; will alter the topological connectivity of loops and attached chains° For example, row …","PeriodicalId":109454,"journal":{"name":"ACM '59","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1959-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116865827","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":"Information storage and retrieval","authors":"Susan Brewer","doi":"10.1145/612201.612221","DOIUrl":"https://doi.org/10.1145/612201.612221","url":null,"abstract":"The letter and/or sound combinations that make up a human language are limited by the human's ability to pronounce tnese sounds° Therefore, the standard library search, which as a rule looks for all possible combinations of letters to find a word, is wasteful. Certain letters simply cannot be followed by certain other letters and a search for them is senseless. Following this same line of reasoning, letters very frequently occur in the combinations that are germane to the particular language. The growing amount of alphanumeric information presently being stored on magnetic tape presents increasingly difficult problems in both the number of tape reels used and the time necessary to search this mass of information in order to extract pertinent literature. At the present time most of this literature on tape utilizes the standard IBM 6-bit code to express alphanumeric symbols. ~t is entirely feasible to record standard English literature on tape -be it professional abstracts or novels -using only approximately two-thirds of the binary bits utilized to represent the same piece of written material in the conventional code. This can be accomplished by setting up, in a 9-bit code, the 400-odd letter combinations occurring most frequently. A 9-bit representation allows the programmer to set up as many as 512 symbols, thus leaving sufficient leeway to assign symbols to the most frequentlyused words, mathematical symbols, professional expressions, that are expected to be encountered in the literature to be recorded. In addition, these relatively short 9-bit symbols can be assigned to all key words that it may be necessary to look for later, thereby accelerating any future library search.","PeriodicalId":109454,"journal":{"name":"ACM '59","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1959-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126322897","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":"Error stability in finite mantissa floating point computers","authors":"J. K. Casey","doi":"10.1145/612201.612263","DOIUrl":"https://doi.org/10.1145/612201.612263","url":null,"abstract":"Floating point computing machines if operating perfectly depart from the ideal macazine in that the exponent is confined to a fixed number of places and that the mantissa is also confined to a fixed number of places° The former restriction leads to overflow and underflow problems and the latter leads to the generation of round off error. We are not concerned here with overflow or underflow problems. We shall be concerned only with the generation of round off error and its effect on the propagation of error. We assume that the round off error generated is that produced automatically by the machine truncating the true resultant of a normalized floa ting point ope ration. By relative error is meant the absolute error (exact resultant minus the machine resultant) divided by the machine resultant. Note that the absolute error referred to includes both the error in the resultant which propagated from the error in the operands as well as the new round off error generated in combining the operands arithmetically. Consider a machine using ~ place mantissas expressed to the base ~. If the resultant of combining two machine, umbers has exponent ~_","PeriodicalId":109454,"journal":{"name":"ACM '59","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1959-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126208321","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":"Critical analysis of data on tenants in low-rent government housing","authors":"G. Urban, H. Appleton, E. Rapke, A. T. Nelms","doi":"10.1145/612201.612222","DOIUrl":"https://doi.org/10.1145/612201.612222","url":null,"abstract":"In accordance with contractual requirements, throughout the notion local Housing authorities conduct an annual status examination of each tenant in federslly~aided or-owned low-rent housiug projects tO determine elJgibili%y for continued occupancyo Approximately 400,000 such re-examinations, centrally edited for inconsistencies~ are the basis of statistical su~aries for agency use and for submittal to Congress. The report form PHA-1245 provides space for a wide variety of data, one line being devoted to each family reexamined , The report includes four items on income~ nine on exemptions, two on rent, three on family composition, supplemented by items on age of family heads racer service-status, unit size~ eligibility statust and by admission darns Any items requiring amplification are accompanied by pertinent remarks, In their ~bility to prepare reports, respondents range from the highly trained statistical specialist in the very large authority to the tenant who devotes a few hours a month to rent collection, tenant selectiont and report preparation, Accordingly, it is difficult to predict the volume and nature of errors likely to occur.","PeriodicalId":109454,"journal":{"name":"ACM '59","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1959-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131251121","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":"On the construction of algorithm translators","authors":"B. Arden","doi":"10.1145/612201.612230","DOIUrl":"https://doi.org/10.1145/612201.612230","url":null,"abstract":"In the exa~pies that follow lo~.~er case letters are floating point variables except i~ J~ and k which ore fixed point integers° Constants are considG~ed as fixed point integer~ if they appear without a docimal point-otherwise floating° Also constants when they appear arc considered ~o be She names of numbers whose values equal the names. The binary operators +~-, / are used in the nor;ual fashion. The multiplication operator (*) is always wrltton~ contiguou3 letters (or leSters separated only by left parentheses) implies subscription (). The expression on the right of the substitution operator (=) defines the new value to be assumed by the verlable on the lefto The statements operated on by current \"formula\" and \"algebraic\" translators such as the statements x(leJ+k) = s+bee+3°l~+(a-b)*c/d, are algorithmic statements in that they describe a procedure for determining a value° The role of the translator program is to produce a set of machine instructions which are equivalent to the original algorithmic statement° I. Statement Decomposition° A co~m-non approach to this task is to first reduce the statement to some standard form which is more directly translatable to machine lan~zuage. For state:~onts h~ving an slgebralc form such as the one above the diegra~atic \"logical tree\" sugDests itself.","PeriodicalId":109454,"journal":{"name":"ACM '59","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1959-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133085567","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}