In this paper we collate and discuss some results on the sparsity structure of a matrix. If a matrix is irreducible, Gaussian elimination yields an LU factorization in which L has at least one entry beneath the diagonal in every column except the last and U has at least one entry to the right of the diagonal in every row except the last. If this factorization is used to solve the equation Ax=b, the intermediate vector has an entry in its last component and the solution x is full. Furthermore, the inverse of A is full.Where the matrix is reducible, these results are applicable to the diagonal blocks of its block triangular form.
{"title":"Sparsity structure and Gaussian elimination","authors":"I. S. Duff, A. Erisman, C. Gear, John Reid","doi":"10.1145/47917.47918","DOIUrl":"https://doi.org/10.1145/47917.47918","url":null,"abstract":"In this paper we collate and discuss some results on the sparsity structure of a matrix. If a matrix is irreducible, Gaussian elimination yields an LU factorization in which L has at least one entry beneath the diagonal in every column except the last and U has at least one entry to the right of the diagonal in every row except the last. If this factorization is used to solve the equation Ax=b, the intermediate vector has an entry in its last component and the solution x is full. Furthermore, the inverse of A is full.Where the matrix is reducible, these results are applicable to the diagonal blocks of its block triangular form.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"1 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":"115199834","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}
The ANSI Standards Subcommittee X3J3 on Fortran has recently completed a draft proposed standard for the Fortran programming language. The draft proposed standard, known informally as Fortran 8x, is a revision of the current standard X3.9-1978, known informally as Fortran 77. This report is a review of Fortran 8x and consists of a series of six articles. The first article gives a general overview of Fortran 8x. The next three articles give brief discussions of the array facilities; the enhanced numeric facilities; and user-defined data types, procedure interfaces, and the new program unit called a module. The fifth article provides a brief analysis of the controversial issues discussed by X3J3 (including both the accepted and rejected facilities for Fortran 8x). The sixth article gives a brief comparison with Ada. The report concludes with a summary giving information on how and where to express opinions of the draft proposed standard.
{"title":"A review and analysis of Fortran 8x","authors":"Brian T. Smith","doi":"10.1145/47917.47923","DOIUrl":"https://doi.org/10.1145/47917.47923","url":null,"abstract":"The ANSI Standards Subcommittee X3J3 on Fortran has recently completed a draft proposed standard for the Fortran programming language. The draft proposed standard, known informally as Fortran 8x, is a revision of the current standard X3.9-1978, known informally as Fortran 77. This report is a review of Fortran 8x and consists of a series of six articles. The first article gives a general overview of Fortran 8x. The next three articles give brief discussions of the array facilities; the enhanced numeric facilities; and user-defined data types, procedure interfaces, and the new program unit called a module. The fifth article provides a brief analysis of the controversial issues discussed by X3J3 (including both the accepted and rejected facilities for Fortran 8x). The sixth article gives a brief comparison with Ada. The report concludes with a summary giving information on how and where to express opinions of the draft proposed standard.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"1 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":"114342704","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}
We have designed a new generation of stiff ordinary differential equation (ODE) solvers for the NAG LIbrary. They replace existing routines which are functionally inferior and have much less user-friendly interfaces. The redesign provides:(i) continuity and stability for users of NAG stiff solvers;(ii) general simplification of interfaces;(iii) new functionality - solving implicit and differential/algebraic systems;(iv) flexibly structured open ended software (based on implicit ODE methods) so that adding new integration methods is a simple matter;(v) a design which facilitates using the solvers from other packages;(vi) an interface which permits the solvers to be used at the "assembly language" level in packages written in more "robust" languages than Fortran77 (for example ADA).
{"title":"The stiff integrators in the NAG library","authors":"M. Berzins, R. Brankin, I. Gladwell","doi":"10.1145/47917.47921","DOIUrl":"https://doi.org/10.1145/47917.47921","url":null,"abstract":"We have designed a new generation of stiff ordinary differential equation (ODE) solvers for the NAG LIbrary. They replace existing routines which are functionally inferior and have much less user-friendly interfaces. The redesign provides:(i) continuity and stability for users of NAG stiff solvers;(ii) general simplification of interfaces;(iii) new functionality - solving implicit and differential/algebraic systems;(iv) flexibly structured open ended software (based on implicit ODE methods) so that adding new integration methods is a simple matter;(v) a design which facilitates using the solvers from other packages;(vi) an interface which permits the solvers to be used at the \"assembly language\" level in packages written in more \"robust\" languages than Fortran77 (for example ADA).","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"21 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":"127246932","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}
Over the past few years a number of algorithms for solving large sparse systems of equations on distributed-memory multiprocessors have been developed. In this article the authors point out that the properties of sparse matrix problems generally, along with the characteristics of these parallel algorithms for solving them, lead to inefficient use of memory. An example is presented to show that a (relatively small) amount of shared memory on an otherwise pure distributed-memory multiprocessor is very desirable when it is being used to execute these parallel algorithms.
{"title":"Some shared memory is desirable in parallel sparse matrix computation","authors":"A. George, E. Ng","doi":"10.1145/47917.47919","DOIUrl":"https://doi.org/10.1145/47917.47919","url":null,"abstract":"Over the past few years a number of algorithms for solving large sparse systems of equations on distributed-memory multiprocessors have been developed. In this article the authors point out that the properties of sparse matrix problems generally, along with the characteristics of these parallel algorithms for solving them, lead to inefficient use of memory. An example is presented to show that a (relatively small) amount of shared memory on an otherwise pure distributed-memory multiprocessor is very desirable when it is being used to execute these parallel algorithms.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"54 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":"114572383","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}
This paper is a development of a project assigned to a graduate class in Numerical Methods in the Fall Semester 1980 at USC. This approach to teaching shows some similarities with the Claremont Mathematics Clinic, see [4].
{"title":"Decomposing a sequence of matrices that differ only in one submatrix","authors":"W. Proskurowski","doi":"10.1145/43931.43935","DOIUrl":"https://doi.org/10.1145/43931.43935","url":null,"abstract":"This paper is a development of a project assigned to a graduate class in Numerical Methods in the Fall Semester 1980 at USC. This approach to teaching shows some similarities with the Claremont Mathematics Clinic, see [4].","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127067564","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}
The ANSI Standards Subcommittee X3J3 has recently released the draft proposed Fortran standard [1] for public review. The proposed revision, informally known as Fortran 8x, is being reviewed, beginning October 23, 1987, and ending February 23, 1988. It represents an upward compatible revision of the current standard Fortran 77 [2] in the sense that all Fortran 77 standard-conforming programs conform to the proposed Fortran 8x language.
{"title":"Fortran 8x—its public review","authors":"Brian T. Smith","doi":"10.1145/43931.43932","DOIUrl":"https://doi.org/10.1145/43931.43932","url":null,"abstract":"The ANSI Standards Subcommittee X3J3 has recently released the draft proposed Fortran standard [1] for public review. The proposed revision, informally known as Fortran 8x, is being reviewed, beginning October 23, 1987, and ending February 23, 1988. It represents an upward compatible revision of the current standard Fortran 77 [2] in the sense that all Fortran 77 standard-conforming programs conform to the proposed Fortran 8x language.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"24 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123481749","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}
Familiar forms which may be theoretically monotone may not be evaluated monotonically even with monotone arithmetic.
熟悉的形式在理论上可能是单调的，即使用单调算法也不一定是单调的。
{"title":"Provably monotone approximations, ROMANNUMERAL 3","authors":"C. Dunham","doi":"10.1145/43931.43934","DOIUrl":"https://doi.org/10.1145/43931.43934","url":null,"abstract":"Familiar forms which may be theoretically monotone may not be evaluated monotonically even with monotone arithmetic.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125688810","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}
I recently had occasion to extend a derivative-computation package I had written in 1971 to add the capability of dealing with a function defined implicitly. This led me to see the duality between Taylor series reversion and the chain rule of differentiation of a composite function. I was also struck with the compactness with which these algorithms could be expressed in a programming language, which in my case was Fortran 77. The basic ideas involved will probably not be new to persons who have worked on computerization of symbolic mathematics or other approaches to derivative computation, however, I think this may be of interest to many readers of this newsletter as an instance of a very small body of code implementing a mathematical transformation that might a priori be thought to be somewhat complicated.
{"title":"Series reversion as the reversed chain rule","authors":"C. Lawson","doi":"10.1145/43931.43933","DOIUrl":"https://doi.org/10.1145/43931.43933","url":null,"abstract":"I recently had occasion to extend a derivative-computation package I had written in 1971 to add the capability of dealing with a function defined implicitly. This led me to see the duality between Taylor series reversion and the chain rule of differentiation of a composite function. I was also struck with the compactness with which these algorithms could be expressed in a programming language, which in my case was Fortran 77. The basic ideas involved will probably not be new to persons who have worked on computerization of symbolic mathematics or other approaches to derivative computation, however, I think this may be of interest to many readers of this newsletter as an instance of a very small body of code implementing a mathematical transformation that might a priori be thought to be somewhat complicated.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131437369","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}
A function for generating pseudorandom numbers on programmable calculators is evaluated and found to be deficient.
对可编程计算器上生成伪随机数的函数进行了评估，发现该函数存在缺陷。
{"title":"Note on a pseudorandom number generator","authors":"James F. Fullerton","doi":"10.1145/37523.37524","DOIUrl":"https://doi.org/10.1145/37523.37524","url":null,"abstract":"A function for generating pseudorandom numbers on programmable calculators is evaluated and found to be deficient.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1987-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129436293","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}
The long-hand square root algorithm, when implemented in binary arithmetic, produces immediately the analytic result (as opposed to the successive approximations generated by the Newton-Raphson method). It also uses only addition, subtraction, and bits shifts; it is related to the binary integer division algorithm, but is in fact a simpler procedure.
{"title":"On a fast integer square root algorithm","authors":"T. Rolfe","doi":"10.1145/37523.37525","DOIUrl":"https://doi.org/10.1145/37523.37525","url":null,"abstract":"The long-hand square root algorithm, when implemented in binary arithmetic, produces immediately the analytic result (as opposed to the successive approximations generated by the Newton-Raphson method). It also uses only addition, subtraction, and bits shifts; it is related to the binary integer division algorithm, but is in fact a simpler procedure.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1987-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129429752","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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