ACM '59 Pub Date : 1959-09-01 DOI: 10.1145/612201.612237

P. B. Davenport

{"title":"Reduction of a generalized matrix of polynomial elements to triangular form on the IBM 704","authors":"P. B. Davenport","doi":"10.1145/612201.612237","DOIUrl":"https://doi.org/10.1145/612201.612237","url":null,"abstract":"A new method [1], developed by the author, for reducing matrices with polynomial elements (hereafter referred to as lambda-matrices) to triangular form is presented. The method presented has been programmed on the IBM 704. The process may be used for various applications such as obtaining the characteristic equation of a constant matrix A,| λI-A| = 0, determining the characteristic equation for generalized lambda-matrices such as those which arise in systems of linear differential equations with constant coefficients, and providing a mathematical solution in analytical form of such systems.Existing computer programming methods for obtaining the characteristic equation of lambda-matrices employ some variation of the method of determinants. It is well known that the computing time for such methods increases rapidly as the order of the matrix increases. The method presented requires far fewer operations than determinant methods and although it is equivalent to the division algorithm for polynomials discussed in [2], it has an advantage over this method in that it does not require polynomial division and replaces general polynomial multiplication with a trivial form of this operation.The paper is presented in three sections; (1) the mathematical method employed in the reduction, (2) some special programming techniques, and (3) a brief description of the scaling techniques used.","PeriodicalId":109454,"journal":{"name":"ACM '59","volume":"49 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":"131328376","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}

引用次数: 0

Random number generators 随机数生成器

ACM '59 Pub Date : 1959-09-01 DOI: 10.1145/612201.612203

Martin Greenberger

引用次数: 1

The use of generators in TAC 发电机在TAC中的使用

ACM '59 Pub Date : 1959-09-01 DOI: 10.1145/612201.612274

H. Siegal, James A. Painter

{"title":"The use of generators in TAC","authors":"H. Siegal, James A. Painter","doi":"10.1145/612201.612274","DOIUrl":"https://doi.org/10.1145/612201.612274","url":null,"abstract":"One of the t r a d i t i o n a l d e f i c i e n c i e s of an assembly program has been the necessity to write in a language similar to that used for machine instructions. There are large areas of programming that use standard routines with d i f ferent parameters and linkages. The use of a computer-instruction format makes the expression of these parameters and ]inkages more or less inconvenient~ hence prone to error. The incorporation of macro-instructions and generators into the TRANSAC Assembler-Compiler (TAC) System provides the a b i l i t y to use a language that is more problem-oriented. Input to the generators may be any type of pseudo-code within very broad limits° Output in the form of generated coding may be any type acceptable to TAC, Usually it will be symbolic computer languages but it may contain macro-instruction calls~ subroutine calls~ and even more generator pseudo-codeo There is no limit to the leve]s of nesting of generators. The handling of macro-instructions will be described elsewhere so that we will discuss generators only. Generators may be added~ removed~ or changed at the option of the using installation. Certain basic ones are supplied with the TAC system~ but a primary goal of design for TAC has been flexibility. For this reason~ a general system of handling generators has been developed. The pseudo-code used by the generator can be of whatever form the generator writer wishes~ except that the command field must be a unique","PeriodicalId":109454,"journal":{"name":"ACM '59","volume":"41 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":"114575890","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}

引用次数: 1

The method of spherical harmonics as applied to the one-velocity boltzmann equation in infinite cylinders 应用球谐法求解无限圆柱体中单速度玻尔兹曼方程

ACM '59 Pub Date : 1959-09-01 DOI: 10.1145/612201.612267

G. Goertzel, H. V. Waldinger, J. Agresta

引用次数: 0

Automatic programming for real-time computers 用于实时计算机的自动编程

ACM '59 Pub Date : 1959-09-01 DOI: 10.1145/612201.612277

W. T. Comfort, H. H. Bloem

{"title":"Automatic programming for real-time computers","authors":"W. T. Comfort, H. H. Bloem","doi":"10.1145/612201.612277","DOIUrl":"https://doi.org/10.1145/612201.612277","url":null,"abstract":"A digital control s y s t e m consists of 3 basic sections: sensing devices~ digital computer, and controlling devices° A closed loop is f o r m e d through the external environment, w h e r e b y the sensing devices provide information to the c o m p u t e r so that it can monitor and control the opera~ tion of the controlling devices, and thus control the system. A large part of the p r o b l e m of specifying the computational requirements for a s y s t e m consists of defining a mathematical m o d e l of the system° Just as important, however, is the job of defining the control capabilities of the computer, and this changes the p r o b l e m f r o m a simple equation evaluation p r o g r a m to a c o m p l e x logical p r o g r a m. A s a result, a detailed flow d i a g r a m of the whole p r o b l e m has been found indispensable. The C o m p u t e r and P r o g r a m m i n g The control computer can be classified as a general purpose machine. Because of its airborne application, however, there are imposing size and weight limitations which m a k e p r o g r a m m i n g considerably m o r e difficult than would otherwise be the case. In particular, there is a very difficult d r u m latency p r o b l e m to be coped with. To help relieve s o m e of the inherent problems, various p r o g r a m m i n g techniques have been developed utilizing the I B M 704 E D P M. The Symbolic P r o g r a m m e r R A P F O D I A D is a symbolic a s s e m b l y p r o g r a m to be used on the 704 to generate p r o g r a m s for the control s y s t e m computer. Input to …","PeriodicalId":109454,"journal":{"name":"ACM '59","volume":"8 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":"125075495","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}

引用次数: 6

New merge sorting techniques 新的归并排序技术

ACM '59 Pub Date : 1959-09-01 DOI: 10.1145/612201.612219

B. K. Betz, W. Carter

引用次数: 7

Simpson's rule for an odd number of intervals 关于奇数区间的辛普森法则

ACM '59 Pub Date : 1959-09-01 DOI: 10.1145/612201.612205

Jack Hollingsworth, H. F. Hunter

引用次数: 4

On the coding of Jacobi's method of computing eigenvalues and eigenvectors of real, symmetric matrices 实对称矩阵计算特征值和特征向量的Jacobi方法的编码

ACM '59 Pub Date : 1959-09-01 DOI: 10.1145/612201.612241

F. J. Corbató