{"title":"Improvement of complex arithmetic by use of double elements","authors":"C. Dunham","doi":"10.1145/74654.74655","DOIUrl":"https://doi.org/10.1145/74654.74655","url":null,"abstract":"It is shown that use of double precision in complex multiplication and division can significantly reduce rounding errors in these operations. Use of double precision accumulation of inner products in complex multiplication gives very close to the best possible error bound. Use of the same in complex division reduces error bounds, but a double precision divide is necessary to get close to the best possible bound.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"241 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133714408","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":"Some statistics on Gaussian elimination with partial pivoting","authors":"A. MacLeod","doi":"10.1145/74650.74653","DOIUrl":"https://doi.org/10.1145/74650.74653","url":null,"abstract":"There has recently been an upsurge of work on the (by now) classical problem of the stability of Gaussian elimination e.g., the papers of Trefethen & Schreiber [5], and Higham and Higham [2]. This short note describes some experimental results in this area derived by the author. They are described more fully in a technical report [4].","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121801804","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 philosophy for scientific computing tools","authors":"W. M. Coughran, E. Grosse","doi":"10.1145/74650.74651","DOIUrl":"https://doi.org/10.1145/74650.74651","url":null,"abstract":"We argue that subroutine libraries are not enough but need to be supplemented by common file formats and directly executable commands. A concrete example, tensor spline primitives, illustrates this style of programming.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123191109","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":"Perturbation analysis of Horner's method for nice cases","authors":"C. Dunham","doi":"10.1145/74650.74652","DOIUrl":"https://doi.org/10.1145/74650.74652","url":null,"abstract":"Under favourable conditions, evaluation of polynomials by Homer's rule has an error not exceeding a few units in the last place.It has been observed that for moderate sized x and coefficients decreasing rapidly in magnitude that floating point evaluation of polynomials by Homer's method gives results accurate to around one or two units in the last place. A hand calculated example together with an informal justification is given by Fike (1968, pp. 52--53). In this note the observation is justified by a Wilkinson-type backward error analysis. It would be helpful for the reader to be familiar with the approach of Wilkinson (1963, Chap. 1), in which fl (expr) denotes the effect of evaluation of expression expr in floating point.We will assume that floating point is done using guard digits (Johnston, 1982, p. 11: Sterbenz, 1974) in which case we have by analysis similar to those of Wilkinson (1963, Chap. 1).","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116810498","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":"Solving equations nonlinear in only one of N + 1 variables","authors":"C. Dunham, C. Zhu","doi":"10.1145/58859.58860","DOIUrl":"https://doi.org/10.1145/58859.58860","url":null,"abstract":"Equations linear in n out of n + 1 variables can be solved by reduction to a linear subproblem and variation of the nonlinear parameter.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122191352","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":"GAMS, a user's guide","authors":"A. Brook, David Kendrick, A. Meeraus","doi":"10.1145/58859.58863","DOIUrl":"https://doi.org/10.1145/58859.58863","url":null,"abstract":"The most widely used is GAMS, which is specifically designed for Further details on GAMS can be found in the GAMS User's Guide. The GAMS User's Guide. Mathematical Programming, 87:153–176, 2000. (4). A. Brooke, D. Kendrick, and A. Meeraus. GAMS: A User's Guide. The Scientific Press, South San Francisco. JuMP is an open-source modeling language that allows users to express a wide D. Kendrick, A. Meeraus, and R. Raman, GAMS: A User's Guide, Scientific.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133653999","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 use of forward difference equations in animation of physical phenomena","authors":"S. Cynar","doi":"10.1145/58859.58861","DOIUrl":"https://doi.org/10.1145/58859.58861","url":null,"abstract":"In the entertainment industry graphical images are often produced without adherence to physically accurate models. This is usually the case because there is a need to reduce production time and costs. The physical scientist, on the other hand, must produce graphical images that are accurate simulations of the physical phenomena they are attempting to visualize. Frequently the data that an accurate simulation produces can be difficult to use for rendering the animation. This paper describes the use of numerical methods to minimize the number of keyframes for an accurate animation.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"308 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131969609","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":"New version of MACHAR available","authors":"W. Cody","doi":"10.1145/58859.58862","DOIUrl":"https://doi.org/10.1145/58859.58862","url":null,"abstract":"","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116088090","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":"Approximation with exact Lagrange-type interpolation","authors":"C. Dunham, Z. Zhu","doi":"10.1145/47917.47920","DOIUrl":"https://doi.org/10.1145/47917.47920","url":null,"abstract":"Under stated favorable conditions, the Lagrange formula for polynomial interpolation is computationally exact at the nodes. This is applied to approximation with Lagrange-type interpolation.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"788 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113995422","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":"Generations of permutations with non-unique elements","authors":"T. Rolfe","doi":"10.1145/47917.47922","DOIUrl":"https://doi.org/10.1145/47917.47922","url":null,"abstract":"We wish to generate all unique permutations of a list of elements with possibly repeated items. We develop four algorithms to generate permutations, two from Knuth's Art of Computer Programming and two of our own devising. The last one developed also gives a numbering scheme for permutations that can be inverted to regenerate original permutations.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132054977","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}
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