International Symposium on Symbolic and Algebraic Computation最新文献_第8页

Maximum likelihood geometry in the presence of data zeros 存在数据零的最大似然几何

International Symposium on Symbolic and Algebraic Computation Pub Date : 2013-10-15 DOI: 10.1145/2608628.2608659

Elizabeth Gross, J. Rodriguez

引用次数: 25

Evaluating parametric holonomic sequences using rectangular splitting 用矩形分裂评价参数完整序列

International Symposium on Symbolic and Algebraic Computation Pub Date : 2013-10-14 DOI: 10.1145/2608628.2608629

Fredrik Johansson

引用次数: 9

On the complexity of solving bivariate systems: the case of non-singular solutions 二元系统解的复杂性:非奇异解的情况

International Symposium on Symbolic and Algebraic Computation Pub Date : 2013-06-26 DOI: 10.1145/2465506.2465950

R. Lebreton, E. Mehrabi, É. Schost

引用次数: 15

The termination of the F5 algorithm revisited F5算法的终止问题再次被讨论

International Symposium on Symbolic and Algebraic Computation Pub Date : 2013-06-26 DOI: 10.1145/2465506.2465520

Senshan Pan, Yu-pu Hu, Baocang Wang

引用次数: 8

The complexity of factoring univariatepolynomials over the rationals: tutorial abstract 单变量多项式在有理数上因式分解的复杂性:教程摘要

International Symposium on Symbolic and Algebraic Computation Pub Date : 2013-06-26 DOI: 10.1145/2465506.2479779

M. V. Hoeij

引用次数: 0

On the integration of differential fractions 关于微分分数的积分

International Symposium on Symbolic and Algebraic Computation Pub Date : 2013-06-26 DOI: 10.1145/2465506.2465934

François Boulier, F. Lemaire, G. Regensburger, M. Rosenkranz

引用次数: 6

Computing rational solutions of linear matrix inequalities 计算线性矩阵不等式的有理解

International Symposium on Symbolic and Algebraic Computation Pub Date : 2013-06-26 DOI: 10.1145/2465506.2465949

Q. Guo, M. S. E. Din, L. Zhi

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引用次数: 14

Integrability conditions for parameterized linear difference equations 参数化线性差分方程的可积性条件

International Symposium on Symbolic and Algebraic Computation Pub Date : 2013-06-26 DOI: 10.1145/2465506.2465942

Mariya Bessonov, A. Ovchinnikov, M. Shapiro

引用次数: 3

Critical point methods and effective real algebraic geometry: new results and trends 临界点方法与有效实代数几何:新结果与新趋势

International Symposium on Symbolic and Algebraic Computation Pub Date : 2013-06-26 DOI: 10.1145/2465506.2465928

M. S. E. Din

{"title":"Critical point methods and effective real algebraic geometry: new results and trends","authors":"M. S. E. Din","doi":"10.1145/2465506.2465928","DOIUrl":"https://doi.org/10.1145/2465506.2465928","url":null,"abstract":"Critical point methods are at the core of the interplay between polynomial optimization and polynomial system solving over the reals. These methods are used in algorithms for solving various problems such as deciding the existence of real solutions of polynomial systems, performing one-block real quantifier elimination, computing the real dimension of the solution set, etc. The input consists of $s$ polynomials in $n$ variables of degree at most $D$. Usually, the complexity of the algorithms is $(s, D)^{O(n^alpha)}$ where $alpha$ is a constant. In the past decade, tremendous efforts have been deployed to improve the exponents in the complexity bounds. This led to efficient implementations and new geometric procedures for solving polynomial systems over the reals that exploit properties of critical points. In this talk, we present an overview of these techniques and their impact on practical algorithms. Also, we show how we can tune them to exploit algebraic and geometric structures in two fundamental problems. The first one is real root finding of determinants of $n$-variate linear matrices of size $ktimes k$. We introduce an algorithm whose complexity is polynomial in ${{n+k}choose{k}}$ (joint work with S. Naldi and D. Henrion). This improves the previously known $k^{O(n)}$ bound. The second one is about computing the real dimension of a semi-algebraic set. We present a probabilistic algorithm with complexity $(s, D)^{O(n)}$, that improves the long-standing $(s, D)^{O(n^2)}$ bound obtained by Koi-ran (joint work with E. Tsigaridas).","PeriodicalId":243282,"journal":{"name":"International Symposium on Symbolic and Algebraic Computation","volume":"34 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128601916","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

Computer algebra: a 32-year update 计算机代数:32年的更新

International Symposium on Symbolic and Algebraic Computation Pub Date : 2013-06-26 DOI: 10.1145/2465506.2465930

S. Wolfram

引用次数: 4