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
Polynomial-time algorithm for Hilbert series of Borel type ideals Borel型理想Hilbert级数的多项式时间算法
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277516
A. Hashemi
{"title":"Polynomial-time algorithm for Hilbert series of Borel type ideals","authors":"A. Hashemi","doi":"10.1145/1277500.1277516","DOIUrl":"https://doi.org/10.1145/1277500.1277516","url":null,"abstract":"In this paper, it is shown that the Hilbert series of a Borel type ideal may be computed within a complexity which is polynomial in <i>D</i><sup>n</sup> where <i>n</i> + 1 is the number of unknowns and <i>D</i> is the highest degree of a minimal generator of input (monomial) ideal.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121445476","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: 2
Computing monodromy groups defined by plane algebraic curves 计算平面代数曲线定义的单群
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277509
A. Poteaux
{"title":"Computing monodromy groups defined by plane algebraic curves","authors":"A. Poteaux","doi":"10.1145/1277500.1277509","DOIUrl":"https://doi.org/10.1145/1277500.1277509","url":null,"abstract":"We present a symbolic-numeric method to compute the monodromy group of a plane algebraic curve viewed as a ramified covering space of the complex plane. Following the definition, our algorithm is based on analytic continuation of algebraic functions above paths in the complex plane. Our contribution is three-fold : first of all, we show how to use a minimum spanning tree to minimize the length of paths ; then, we propose a strategy that gives a good compromise between the number of steps and the truncation orders of Puiseux expansions, obtaining for the first time a complexity result about the number of steps; finally, we present an efficient numerical-modular algorithm to compute Puiseux expansions above critical points,which is a non trivial task.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128938830","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: 30
A Macaulay 2 package for computing sum of squares decompositions of polynomials with rational coefficients 计算有理系数多项式平方和分解的Macaulay 2包
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277534
Helfried Peyrl, P. Parrilo
{"title":"A Macaulay 2 package for computing sum of squares decompositions of polynomials with rational coefficients","authors":"Helfried Peyrl, P. Parrilo","doi":"10.1145/1277500.1277534","DOIUrl":"https://doi.org/10.1145/1277500.1277534","url":null,"abstract":"In recent years semideffinite programming (SDP) has become the standard technique for computing sum of squares (SOS) decompositions of nonnegative polynomials. Due to the nature of the underlying methods, the solutions are computed numerically, and thus are never exact. In this paper we present a software package for Macaulay 2, which aims at computing an exact SOS decomposition from a numerical solution.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126716379","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
A hybrid integral for parametrized rational functions 参数化有理函数的混合积分
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277531
H. Kai, N. Nakagawa, M. Noda
{"title":"A hybrid integral for parametrized rational functions","authors":"H. Kai, N. Nakagawa, M. Noda","doi":"10.1145/1277500.1277531","DOIUrl":"https://doi.org/10.1145/1277500.1277531","url":null,"abstract":"We present a hybrid integral to obtain symbolic results of an indefinite integral where the integrand is an univariate rational function whose coeficients have a parameter. We consider calculating power series roots of the denominator polynomial by applying Hensel construction. Accurate numerical results for a definite integral are easily obtained by simple substitutions of upper and lower bounds of integral into obtained approximate symbolic results.Numerical experiments show that the hybrid integral works well around the expansion point of the power series roots.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130366640","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
Geometric applications of the Bezout matrix in the Lagrange basis Bezout矩阵在拉格朗日基中的几何应用
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277511
D. Aruliah, Robert M Corless, L. González-Vega, A. Shakoori
{"title":"Geometric applications of the Bezout matrix in the Lagrange basis","authors":"D. Aruliah, Robert M Corless, L. González-Vega, A. Shakoori","doi":"10.1145/1277500.1277511","DOIUrl":"https://doi.org/10.1145/1277500.1277511","url":null,"abstract":"Using a new formulation of the Bézout matrix, we construct bivariate matrix polynomials expressed in a tensor-product Lagrange basis. We use these matrix polynomials to solve common tasks in computer-aided geometric design. For example, we show that these bivariate polynomials can serve as stable and efficient implicit representations of plane curves for a variety of curve intersection problems.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130367730","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: 19
Lower bounds for approximate factorizations via semidefinite programming: (extended abstract) 半定规划近似分解的下界:(扩展抽象)
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277532
E. Kaltofen, Bin Li, K. Sivaramakrishnan, Zhengfeng Yang, L. Zhi
{"title":"Lower bounds for approximate factorizations via semidefinite programming: (extended abstract)","authors":"E. Kaltofen, Bin Li, K. Sivaramakrishnan, Zhengfeng Yang, L. Zhi","doi":"10.1145/1277500.1277532","DOIUrl":"https://doi.org/10.1145/1277500.1277532","url":null,"abstract":"The problem of approximately factoring a real or complex multivariate polynomial f seeks minimal perturbations ? f to the coefficients of the input polynomial f so that the deformed polynomial f +Δ f has the desired factorization properties. Effcient algorithms exist that compute the nearest real or complex polynomial that has non-trivial factors (see [3,6 ]and the literature cited there). Here we consider the solution of the arising optimization problems polynomial optimization (POP)via semide finite programming (SDP). We restrict to real coe cients in the input and output polynomials.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123293196","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: 2
From quotient-difference to generalized eigenvalues and sparse polynomial interpolation 从商差到广义特征值和稀疏多项式插值
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277518
Wen-shin Lee
{"title":"From quotient-difference to generalized eigenvalues and sparse polynomial interpolation","authors":"Wen-shin Lee","doi":"10.1145/1277500.1277518","DOIUrl":"https://doi.org/10.1145/1277500.1277518","url":null,"abstract":"The numerical quotient-difference algorithm,or the qd-algorithm, can be used for determining the poles of a meromorphic function directly from its Taylor coeffcients. We show that the poles computed in the qd-algorithm, regardless of their multiplicities,are converging to the solution of a generalized eigenvalue problem. In a special case when all the poles are simple,such generalized eigenvalue problem can be viewed as a reformulation of Prony 's method,a method that is closely related to the Ben-Or/Tiwari algorithm for interpolating a multivariate sparse polynomial in computer algebra.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122027442","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: 11
Companion matrix pencils for hermite interpolants 埃尔米特插值的同伴矩阵铅笔
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277529
D. Aruliah, Robert M Corless, L. González-Vega, A. Shakoori
{"title":"Companion matrix pencils for hermite interpolants","authors":"D. Aruliah, Robert M Corless, L. González-Vega, A. Shakoori","doi":"10.1145/1277500.1277529","DOIUrl":"https://doi.org/10.1145/1277500.1277529","url":null,"abstract":"This abstract describes new methods for solving polynomial problems where the polynomials are expressed as (generalized) Hermite interpolants; that is, where the polynomials are given by values and by derivatives at certain nodes. We consider here the mixed case where at some nodes, only values are known, whereas at others, both values and derivatives are known. We neither consider the case where derivatives higher than the 1st are known, nor the Birkhoff case where some data is ‘missing’. In the full paper, we will give the general case for higher derivatives; we leave the Birkhoff case for a future paper. For example, suppose that we know that a polynomial has the values p(tm) = pm, p(tm+1/2) = pm+1/2, and p(tm+1) = pm+1, for distinct nodes τ1 = tm, τ2 = tm+1/2, τ3 = tm+1, and suppose further that we also know the derivatives p′(tm) and p′(tm+1), which we denote p ′ m and p ′ m+1. This can occur naturally in the context of the numerical solution of initial value problems for ordinary differential equations, for example. At the beginning of a numerical step, t = tm, the value is known and the derivative is calculated by a function evaluation, so we know pm and p ′ m. At the end of the step, t = tm+1, another function evaluation is carried out in order to continue the marching process and so we know p′m+1 as well as pm+1. However, it is not necessarily the case that derivatives are known in the interior of the interval (tm, tm+1), although for graphical and other purposes the values of the polynomial p(t) interpolating the numerical","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130864352","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
On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms 符号-数值混合算法随机化的概率分析
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277503
E. Kaltofen, Zhengfeng Yang, L. Zhi
{"title":"On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms","authors":"E. Kaltofen, Zhengfeng Yang, L. Zhi","doi":"10.1145/1277500.1277503","DOIUrl":"https://doi.org/10.1145/1277500.1277503","url":null,"abstract":"Algebraic randomization techniques can be applied to hybrid symbolic-numeric algorithms. Here we consider the problem of interpolating a sparse rational function from noisy values. We develop a new hybrid algorithm based on Zippel's original sparse polynomial interpolation technique. We show experimentally that our algorithm can handle sparse polynomials with large degrees. We also give a (partial) mathematical justification why the Zippel's algebraic randomization technique can be used with our approximate data: the randomly generated non-zero values are expected to be bounded away from zero. We show that the random Fourier-like matrices arising in our algorithm, have the desired rank property in the exact case, and appear usable numerically.\u0000 Algebraic randomization techniques can be applied to hybrid symbolic-numeric algorithms. Here we consider the problem of interpolating a sparse rational function from noisy values. We develop a new hybrid algorithm based on Zippel's original sparse polynomial interpolation technique. We show experimentally that our algorithm can handle sparse polynomials with large degrees. We also give a (partial) mathematical justification why the Zippel's algebraic randomization technique can be used with our approximate data: the randomly generated non-zero values are expected to be bounded away from zero. We show that the random Fourier-like matrices arising in our algorithm, have the desired rank property in the exact case, and appear usable numerically.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114077314","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: 29
Null space and eigenspace computations with additive preprocessing 加性预处理的零空间和特征空间计算
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277523
V. Pan, Xiaodong Yan
{"title":"Null space and eigenspace computations with additive preprocessing","authors":"V. Pan, Xiaodong Yan","doi":"10.1145/1277500.1277523","DOIUrl":"https://doi.org/10.1145/1277500.1277523","url":null,"abstract":"We propose and analyze additive preprocessing for computing a vector in the null space of a matrix and a basis for this space. Due to our preprocessing, instead of singular linear systems we solve nonsingular ones, which preserve the conditioning properties and the structure of the input matrices. We extend our preprocessing to decrease the size and the condition number of an ill conditioned input matrix. We also cover applications to the eigenspace computations and to generating effective preconditioners for a linear system of equations.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130719634","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: 15
首页 上一页
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