Proceedings of the 2005 international symposium on Symbolic and algebraic computation最新文献_第2页

On computing nearest singular hankel matrices 关于计算最接近的奇异汉克尔矩阵

Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI: 10.1145/1073884.1073909

M. Hitz

引用次数: 6

On using bi-equational constraints in CAD construction 双方程约束在CAD结构中的应用

Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI: 10.1145/1073884.1073897

Christopher W. Brown, S. McCallum

{"title":"On using bi-equational constraints in CAD construction","authors":"Christopher W. Brown, S. McCallum","doi":"10.1145/1073884.1073897","DOIUrl":"https://doi.org/10.1145/1073884.1073897","url":null,"abstract":"This paper introduces an improved method for constructing cylindrical algebraic decompositions (CADs) for formulas with two polynomial equations as implied constraints. The fundamental idea is that neither of the varieties of the two polynomials is actually represented by the CAD the method produces, only the variety defined by their common zeros is represented. This allows for a substantially smaller projection factor set, and for a CAD with many fewer cells.In the current theory of CADs, the fundamental object is to decompose n-space into regions in which a polynomial equation is either identically true or identically false. With many polynomials, one seeks a decomposition into regions in which each polynomial equation is identically true or false independently. The results presented here are intended to be the first step in establishing a theory of CADs in which systems of equations are fundamental objects, so that given a system we seek a decomposition into regions in which the system is identically true or false --- which means each equation is no longer considered independently. Quantifier elimination problems of this form (systems of equations with side conditions) are quite common, and this approach has the potential to bring large problems of this type into the scope of what can be solved in practice. The special case of formulas containing two polynomial equations as constraints is an important one, but this work is also intended to be extended in the future to the more general case.","PeriodicalId":311546,"journal":{"name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129434034","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: 28

On a finite kernel theorem for polynomial-type optimization problems and some of its applications 多项式型优化问题的有限核定理及其一些应用

Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI: 10.1145/1073884.1073887

Wu Wen-tsun

{"title":"On a finite kernel theorem for polynomial-type optimization problems and some of its applications","authors":"Wu Wen-tsun","doi":"10.1145/1073884.1073887","DOIUrl":"https://doi.org/10.1145/1073884.1073887","url":null,"abstract":"Extremalization and optimization problems are considered as of utmost importance both in the past and in the present days. Thus, in the early beginning of infinitesimal calculus the determination of maxima and minima is one of the stimulating problems causing the creation of calculus and one of the successful applications which stimulates its rapid further development. However, the maxima and minima involved are all of local character leading to equations difficult to be solved, not to say the inherent logical difficulties involving necessary and/or sufficient conditions to be satisfied. In recent years owing to creation of computers various kinds of numerical methods have been developed which involve usually some converging processes. These methods, besides such problems as stability or error-control, can hardly give the greatest or least value, or global-optimal value for short over the whole domain, supposed to exist in advance. However, the problem becomes very agreeable if we limit ourselves to the polynomial-type case. In fact, based on the classical treatment of polynomial equations-solving in ancient China and its modernization due to J.F. Ritt, we have discovered a Finite Kernel Theorem to the effect that a finite set of real values, to be called the finite kernel set of the given problem, may be so determined that all possible extremal values will be found among this finite set and the corresponding extremal zeros are then trivially determined. Clearly it will give the global optimal value over the whole domain in consideration, if it is already known to exist in some way. Associated packages wsolve and e_val have been given by D. K. Wang and had been applied with success in various kinds of problems, polynomial-definiteness, non-linear programming, etc., particularly problems involving inequalities.","PeriodicalId":311546,"journal":{"name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125871934","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

Partial degree formulae for rational algebraic surfaces 有理代数曲面的偏次公式

Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI: 10.1145/1073884.1073926

S. Pérez-Díaz, J. Sendra

引用次数: 11

Signature of symmetric rational matrices and the unitary dual of lie groups 对称有理矩阵的签名与李群的酉对偶

Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI: 10.1145/1073884.1073889

Jeffrey Adams, B. D. Saunders, Z. Wan

引用次数: 4

Generalized Loewy-decomposition of d-modules d模的广义loewy分解

Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI: 10.1145/1073884.1073908

D. Grigoriev, F. Schwarz

引用次数: 31

A reliable block Lanczos algorithm over small finite fields 小有限域上可靠的块Lanczos算法

Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI: 10.1145/1073884.1073910

B. Hovinen, W. Eberly

引用次数: 7

Multivariate power series multiplication 多元幂级数乘法

Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI: 10.1145/1073884.1073925

É. Schost

引用次数: 17

Solving second order linear differential equations with Klein's theorem 用克莱因定理求解二阶线性微分方程

Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI: 10.1145/1073884.1073931

M. V. Hoeij, Jacques-Arthur Weil

引用次数: 36

Finding telescopers with minimal depth for indefinite nested sum and product expressions 寻找无限嵌套和和乘积表达式的最小深度的伸缩器

Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI: 10.1145/1073884.1073924

Carsten Schneider

引用次数: 29