发布求助
文献互助 智能选刊 最新文献

Symbolic-Numeric Computation最新文献

筛选
英文 中文
A proof of the monotone column permanent (MCP) conjecture for dimension 4 via sums-of-squares of rational functions 用有理函数的平方和证明4维单调列永久猜想
Symbolic-Numeric Computation Pub Date : 2009-08-03 DOI: 10.1145/1577190.1577204
E. Kaltofen, Zhengfeng Yang, L. Zhi
{"title":"A proof of the monotone column permanent (MCP) conjecture for dimension 4 via sums-of-squares of rational functions","authors":"E. Kaltofen, Zhengfeng Yang, L. Zhi","doi":"10.1145/1577190.1577204","DOIUrl":"https://doi.org/10.1145/1577190.1577204","url":null,"abstract":"For a proof of the monotone column permanent (MCP)conjecture for dimension 4 it is sufficient to show that 4 polynomials, which come from the permanents of real matrices, are nonnegative for all real values of the variables, where the degrees and the number of the variables of these polynomials are all 8. Here we apply a hybrid symbolic-numerical algorithm for certifying that these polynomials can be written as an exact fraction of two polynomial sums-of-squares (SOS) with rational coefficients.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"122 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114906453","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: 18
Continuations and monodromy on random riemann surfaces 随机riemann曲面上的延拓与单性
Symbolic-Numeric Computation Pub Date : 2009-08-03 DOI: 10.1145/1577190.1577210
A. Galligo, A. Poteaux
{"title":"Continuations and monodromy on random riemann surfaces","authors":"A. Galligo, A. Poteaux","doi":"10.1145/1577190.1577210","DOIUrl":"https://doi.org/10.1145/1577190.1577210","url":null,"abstract":"Our main motivation is to analyze and improve factorization algorithms for bivariate polynomials in <b>C</b>[<i>x,y</i>], which proceed by continuation methods.\u0000 We consider a Riemann surface <i>X</i> defined by a polynomial <i>f(x,y)</i> of degree <i>d</i>, whose coefficients are choosen randomly. Hence we can supose that <i>X</i> is smooth, that the discriminant δ(<i>x</i>) of <i>f</i> has <i>d</i>(<i>d</i>-1) simple roots, Δ, that δ(0) ≠ 0 i.e. the corresponding fiber has <i>d</i> distinct points {<i>y</i><sub>1</sub>,...,<i>y</i><sub>d</sub>}. When we lift a loop 0 ∈ γ ⊂ <b>C</b> - Δ by a continuation method, we get <i>d</i> paths in <i>X</i> connecting {<i>y</i><sub>1</sub>,...,<i>y</i><sub>d</sub>}, hence defining a permutation of that set. This is called monodromy.\u0000 Here we present experimentations in Maple to get statistics on the distribution of transpositions corresponding to the loops turning around each point of Δ. Multiplying families of \"consecutive\" transpositions, we construct permutations then subgroups of the symmetric group. This allows us to establish and study experimentally some conjectures on the distribution of these transpositions then on transitivity of the generated subgroups.\u0000 These results provide interesting insights on the structure of such Riemann surfaces (or their union) and eventually can be used to develop fast algorithms.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129737885","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
Parametrization of ε-rational curves: extended abstract ε-有理曲线的参数化:扩展抽象
Symbolic-Numeric Computation Pub Date : 2009-08-03 DOI: 10.1145/1577190.1577221
S. Pérez-Díaz, J. Sendra, Sonia L. Rueda, J. Sendra
{"title":"Parametrization of ε-rational curves: extended abstract","authors":"S. Pérez-Díaz, J. Sendra, Sonia L. Rueda, J. Sendra","doi":"10.1145/1577190.1577221","DOIUrl":"https://doi.org/10.1145/1577190.1577221","url":null,"abstract":"In this talk we deal with the problem of parametrizing approximately a perturbed rational affine plane curve implicitly given. We present some of our recent results (see [3], [4], [5], [6]) and we describe our on going research in this context. More precisely, we focus on our approximate parametrization algorithm in [6], and we present an empirical analysis that shows that the input and output curves of the algorithm are close in practice.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121088659","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
Reducing exact computations to obtain exact results based on stabilization techniques 减少精确计算以获得基于稳定技术的精确结果
Symbolic-Numeric Computation Pub Date : 2009-08-03 DOI: 10.1145/1577190.1577219
Kiyoshi Shirayanagi, Hiroshi Sekigawa
{"title":"Reducing exact computations to obtain exact results based on stabilization techniques","authors":"Kiyoshi Shirayanagi, Hiroshi Sekigawa","doi":"10.1145/1577190.1577219","DOIUrl":"https://doi.org/10.1145/1577190.1577219","url":null,"abstract":"For a certain class of algebraic algorithms, we propose a new method that reduces the number of exact computational steps needed for obtaining exact results. This method is the floating-point interval method using zero rewriting and symbols. Zero rewriting, which is from stabilization techniques, rewrites an interval coefficient into the zero interval if the interval contains zero. Symbols are used to keep track of the execution path of the original algorithm with exact computations, so that the associated real coefficients can be computed by evaluating the symbols. The key point is that at each stage of zero rewriting, one checks to see if the zero rewriting is really correct by exploiting the associated symbol. This method mostly uses floating-point computations; the exact computations are only performed at the stage of zero rewriting and in the final evaluation to get the exact coefficients. Moreover, one does not need to check the correctness of the output.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"135 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114367871","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: 7
An effective implementation of a symbolic-numeric cylindrical algebraic decomposition for quantifier elimination 一种用于量词消去的符号-数值圆柱代数分解的有效实现
Symbolic-Numeric Computation Pub Date : 2009-08-03 DOI: 10.1145/1577190.1577203
Hidenao Iwane, H. Yanami, H. Anai, K. Yokoyama
{"title":"An effective implementation of a symbolic-numeric cylindrical algebraic decomposition for quantifier elimination","authors":"Hidenao Iwane, H. Yanami, H. Anai, K. Yokoyama","doi":"10.1145/1577190.1577203","DOIUrl":"https://doi.org/10.1145/1577190.1577203","url":null,"abstract":"Recently quantifier elimination (QE) has been of great interest in many fields of science and engineering. In this paper an effective symbolic-numeric cylindrical algebraic decomposition (SNCAD) algorithm and its variant specially designed for QE are proposed based on the authors' previous work and our implementation of those is reported. Based on analysing experimental performances, we are improving our design/synthesis of the SNCAD for its practical realization with existing efficient computational techniques and several newly introduced ones. The practicality of the SNCAD is now examined by a number of experimental results including practical engineering problems, which also reveals the quality of the implementation.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122955191","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: 44
Nearly optimal symbolic-numerical algorithms for structured integer matrices and polynomials 结构整数矩阵和多项式的近最优符号-数值算法
Symbolic-Numeric Computation Pub Date : 2009-08-03 DOI: 10.1145/1577190.1577209
V. Pan, B. Murphy, R. Rosholt
{"title":"Nearly optimal symbolic-numerical algorithms for structured integer matrices and polynomials","authors":"V. Pan, B. Murphy, R. Rosholt","doi":"10.1145/1577190.1577209","DOIUrl":"https://doi.org/10.1145/1577190.1577209","url":null,"abstract":"Our unified superfast algorithms for solving Toeplitz, Hankel, Vandermonde, Cauchy, and other structured linear systems of equations with integer coefficients combine Hensel's symbolic lifting and numerical iterative refinement and run in nearly optimal randomized Boolean time for both solution and its correctness verification. The algorithms and nearly optimal time bounds are extended to some fundamental computations with univariate polynomials that have integer coefficients. Furthermore, we develop lifting modulo powers of two to implement our algorithms in the binary mode within a fixed precision.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126807037","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: 3
Curve/surface intersection problem by means of matrix representations 用矩阵表示曲线/曲面的相交问题
Symbolic-Numeric Computation Pub Date : 2009-08-03 DOI: 10.1145/1577190.1577205
Thang Luu Ba, Laurent Busé, B. Mourrain
{"title":"Curve/surface intersection problem by means of matrix representations","authors":"Thang Luu Ba, Laurent Busé, B. Mourrain","doi":"10.1145/1577190.1577205","DOIUrl":"https://doi.org/10.1145/1577190.1577205","url":null,"abstract":"In this paper, we introduce matrix representations of algebraic curves and surfaces for Computer Aided Geometric Design (CAGD). The idea of using matrix representations in CAGD is quite old. The novelty of our contribution is to enable non square matrices, extension which is motivated by recent research in this topic. We show how to manipulate these representations by proposing a dedicated algorithm to address the curve/surface intersection problem by means of numerical linear algebra techniques.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128647500","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: 17
Computing nearest Gcd with certification 计算最近的Gcd认证
Symbolic-Numeric Computation Pub Date : 2009-08-03 DOI: 10.1145/1577190.1577200
Guillaume Chèze, Jean-Claude Yakoubsohn, A. Galligo, B. Mourrain
{"title":"Computing nearest Gcd with certification","authors":"Guillaume Chèze, Jean-Claude Yakoubsohn, A. Galligo, B. Mourrain","doi":"10.1145/1577190.1577200","DOIUrl":"https://doi.org/10.1145/1577190.1577200","url":null,"abstract":"A bisection method, based on exclusion and inclusion tests, is used to address the nearest univariate gcd problem formulated as a bivariate real minimization problem of a rational fraction.\u0000 The paper presents an algorithm, a first implementation and a complexity analysis relying on Smale's α-theory. We report its behavior on an illustrative example.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"128 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132085500","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: 5
Computing multivariate approximate GCD based on Barnett's theorem 基于Barnett定理的多元近似GCD计算
Symbolic-Numeric Computation Pub Date : 2009-08-03 DOI: 10.1145/1577190.1577214
Masaru Sanuki
{"title":"Computing multivariate approximate GCD based on Barnett's theorem","authors":"Masaru Sanuki","doi":"10.1145/1577190.1577214","DOIUrl":"https://doi.org/10.1145/1577190.1577214","url":null,"abstract":"We present algorithms for multivariate GCD and approximate GCD by modifying Barnett's theorem, which is based on the LU-decomposition of Bézout matrix. Our method is suited for multivariate polynomials with large degrees. Also, we analyze ill-conditioned cases of our method. We show our method is stabler and faster than many other methods.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121065310","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: 3
Convergence and many-valuedness of hensel seriesnear the expansion point 膨胀点附近自身级数的收敛性和多值性
Symbolic-Numeric Computation Pub Date : 2009-08-03 DOI: 10.1145/1577190.1577215
Tateaki Sasaki, D. Inaba
{"title":"Convergence and many-valuedness of hensel seriesnear the expansion point","authors":"Tateaki Sasaki, D. Inaba","doi":"10.1145/1577190.1577215","DOIUrl":"https://doi.org/10.1145/1577190.1577215","url":null,"abstract":"Hensel series is an expansion of multivariate algebraic function at a singular point, computed from the defining polynomial by the Hensel construction. The Hensel series is well-structured and tractable, hence it seems to be useful in various applications. In SNC'07, the present authors reported the following interesting properties of Hensel series, which were found numerically. 1) The convergence and the divergence domains co-exist in any small neighborhood of the expansion point. 2) If we trace a Hensel series by passing a divergence domain, the series may jump from a branch to another branch of the original algebraic function. In this paper, we clarify these properties theoretically and derive stronger properties.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117030456","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: 5
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信