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A fast hermite transform with applications to protein structure determination 一种快速hermite变换及其在蛋白质结构测定中的应用
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277519
Gregory Leibon, D. Rockmore, G. Chirikjian
{"title":"A fast hermite transform with applications to protein structure determination","authors":"Gregory Leibon, D. Rockmore, G. Chirikjian","doi":"10.1145/1277500.1277519","DOIUrl":"https://doi.org/10.1145/1277500.1277519","url":null,"abstract":"We discuss algorithms for a fast and stable approximation of the Hermite transform of a compactly supported function on the real line, attainable via an application of a fast algebraic algorithm for computing sums associated to a three-term relation. Trade-offs between approximation in bandwidth (in the Hermite sense) and size of the support region are addressed. Generalizations to any family of orthogonal polynomials are outlined. Applications to the determination of protein structure are discussed.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"65 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":"131336527","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
The schur aggregation for solving linear systems of equations 求解线性方程组的schur聚集
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277522
V. Pan, B. Murphy, R. Rosholt, M. Tabanjeh
{"title":"The schur aggregation for solving linear systems of equations","authors":"V. Pan, B. Murphy, R. Rosholt, M. Tabanjeh","doi":"10.1145/1277500.1277522","DOIUrl":"https://doi.org/10.1145/1277500.1277522","url":null,"abstract":"According to our previous theoretical and experimental study, additive preconditioners can be readily computed for ill conditioned matrices, but application of such preconditioners to facilitating matrix computations is not straight-forward. In the present paper we develop some nontrivial techniques for this task.They enabled us to con ne the original numerical problems to the computation of the Schur aggregates of smaller sizes. We overcome these problems by extending the Wilkinson's iterative re nement and applying some advanced semi-symbolic algorithms for multiplication and summation.In particular with these techniques we control precision throughout our computations.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"51 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":"123015494","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
Numerical optimization in hybrid symbolic-numeric computation 符号-数值混合计算中的数值优化
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277507
L. Zhi
{"title":"Numerical optimization in hybrid symbolic-numeric computation","authors":"L. Zhi","doi":"10.1145/1277500.1277507","DOIUrl":"https://doi.org/10.1145/1277500.1277507","url":null,"abstract":"Approximate symbolic computation problems can be formulated as constrained or unconstrained optimization problems, for example: GCD [3,8,12,13,23], factorization [5,10], and polynomial system solving [2,25,29]. We exploit the special structure of these optimization problems, and show how to design efficient and stable hybrid symbolic-numeric algorithms based on Gauss-Newton iteration, structured total least squares (STLS), semide finite programming and other numeric optimization methods.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"64 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":"123951052","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: 4
Approximate bivariate factorization: a geometric viewpoint 近似二元分解:一个几何观点
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277502
A. Galligo, M. V. Hoeij
{"title":"Approximate bivariate factorization: a geometric viewpoint","authors":"A. Galligo, M. V. Hoeij","doi":"10.1145/1277500.1277502","DOIUrl":"https://doi.org/10.1145/1277500.1277502","url":null,"abstract":"We briefly present and analyze, from a geometric viewpoint, strategies for designing algorithms to factor bivariate approximate polynomials in C[x; y].\u0000 Given a composite polynomial, stably square-free, satisfying a genericity hypothesis, we describe the effect of a perturbation on the roots of its discriminant with respect to one variable, and the perturbation of the corresponding monodromy action on a smooth fiber.\u0000 A novel geometric approach is presented, based on guided projection in the parameter space and continuation method above randomly chosen loops, to reconstruct from a perturbed polynomial a nearby composite polynomial and its irreducible factors. An algorithm and its ingredients are described.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"22 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":"128282173","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: 14
Matched filtering a gravitational wave pulsar signal involving reciprocal gamma functions 匹配过滤引力波脉冲星信号涉及互反伽马函数
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277521
M. Normandin, A. Vajda, S. Valluri
{"title":"Matched filtering a gravitational wave pulsar signal involving reciprocal gamma functions","authors":"M. Normandin, A. Vajda, S. Valluri","doi":"10.1145/1277500.1277521","DOIUrl":"https://doi.org/10.1145/1277500.1277521","url":null,"abstract":"The direct detection of Gravitational Waves (GW) is a challenging problem that involves elaborate experimental and data analysis techniques. The verification of a detected signal demands an effective way to distinguish the source signal from the background noise. One possibility is to perform matched filtering analysis using different templates. Matched filtering, a form of pattern recognition, is ubiquitous and finds innumerable and diverse applications. In the present work, we develop the matched filter analysis for a Fourier transformed, monochromatic, Doppler shifted, continuous GW pulsar signal, which incorporates the effects of the rotational and orbital motion of the Earth. The GW pulsar signal involves a product of the reciprocals of two Eulerian gamma functions containing the Fourier transformed bandwidth frequency in their arguments. We derive an exact analytic solution for the case of constant spectral noise density for the inner product of the template with a received signal, thereby obtaining a closed form expression for the fitting factor, a measure of how well the template matches the received signal. This result can in turn be used to determine the location of the GW source. Simpler cases of the spectral noise density for the French-Italian VIRGO GW detector and its special case for Gaussian white noise are also amenable to an analytic formulation. Our analysis shows that the fitting factor may exhibit simple symmetries with respect to the polar direction angle to the source. Approximate symmetries will also be useful in reducing the numerical computation times. Our current study confirms that the whole analysis lends itself well to parallel computation.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"36 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":"133785472","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
The nearest polynomial with a zero in a given domain 在给定定义域内最接近于零的多项式
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277527
Hiroshi Sekigawa
{"title":"The nearest polynomial with a zero in a given domain","authors":"Hiroshi Sekigawa","doi":"10.1145/1277500.1277527","DOIUrl":"https://doi.org/10.1145/1277500.1277527","url":null,"abstract":"For a real univariate polynomial f and a bounded closed domain D ⊂ C whose boundary <i>C</i> is a simple closed curve of finite length and is represented by a piecewise rational function, we provide a rigorous method for finding the real univariate polynomial <i>f</i> such that <i>f</i> has a zero in <i>D</i> and ||<i>f</i> -- <i>f</i>||∞ is minimal. First, we prove that the absolute value of every coefficient of <i>f</i> -- <i>f</i> is ||<i>f</i> -- <i>f</i>∞ with at most one exception. Using this property and the representation of C, we reduce the problem to solving systems of algebraic equations, each of which consists of two equations with two variables. Furthermore, every equation is of degree one with respect to one of the two variables.","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":"130059815","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: 9
Computing floating-point gröbner bases stably 稳定计算浮点gröbner基数
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277526
Tateaki Sasaki, F. Kako
{"title":"Computing floating-point gröbner bases stably","authors":"Tateaki Sasaki, F. Kako","doi":"10.1145/1277500.1277526","DOIUrl":"https://doi.org/10.1145/1277500.1277526","url":null,"abstract":"Computing floating-point gröbner bases stably.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"101 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":"124831112","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: 32
Border bases of positive dimensional polynomial ideals 正维多项式理想的边界基
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277512
Yufu Chen, X. Meng
{"title":"Border bases of positive dimensional polynomial ideals","authors":"Yufu Chen, X. Meng","doi":"10.1145/1277500.1277512","DOIUrl":"https://doi.org/10.1145/1277500.1277512","url":null,"abstract":"The border bases were generalized to general polynomial ideals (zero and positive dimensional ideals). A new algorithm to compute a border basis for a given polynomial system w.r.t. a specified term order was presented. This algorithm computes a border basis, as well as a reduced Gröbner basis for the polynomial system. A particular eigenvector method to find some components of positive dimensional polynomial systems was sketched too.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"34 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":"125532380","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
Numerical techniques for computing the inertia of products of matrices of rational numbers 计算有理数矩阵积的惯性的数值技术
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277520
Jon P. May, B. D. Saunders, D. Wood
{"title":"Numerical techniques for computing the inertia of products of matrices of rational numbers","authors":"Jon P. May, B. D. Saunders, D. Wood","doi":"10.1145/1277500.1277520","DOIUrl":"https://doi.org/10.1145/1277500.1277520","url":null,"abstract":"Consider a rational matrix, particularly one whose entries have large numerators and denominators, but which is presented as a product of very sparse matrices with relatively small entries. We report on a numerical algorithm which computes the inertia of such a matrix in the nonsingular case and effectively exploits the product structure. We offer a symbolic/numeric hybrid algorithm for the singular case. We compare these methods with previous purely symbolic ones. By \"purely symbolic\" we refer to methods which restrict themselves to exact arithmetic and can assure that errors of approximation do not affect the results. Using an application in the study of Lie Groups as a plentiful source of examples of problems of this nature we explore the relative speeds of the numeric and hybrid methods as well as the range of applicability without error.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"32 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":"131692200","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
Real root-finding 真正root-finding
Symbolic-Numeric Computation Pub Date : 2007-07-25 DOI: 10.1145/1277500.1277524
V. Pan, B. Murphy, R. Rosholt, G. Qian, Y. Tang
{"title":"Real root-finding","authors":"V. Pan, B. Murphy, R. Rosholt, G. Qian, Y. Tang","doi":"10.1145/1277500.1277524","DOIUrl":"https://doi.org/10.1145/1277500.1277524","url":null,"abstract":"In this paper we seek all real roots of a polynomial with real coefficients and real and nonreal roots. Somewhat paradoxically, one of the most effective solutions is by approximating these real roots semi-numerically together with all nonreal roots. Alternative methods are symbolic, based on Descartes' rule of signs (which can be combined with the continued fraction approximation algorithm) or the Sturm (or Sturm-Habicht) sequences. We combine various old and new techniques to devise semi-numerical algorithms that are effective where the real roots do not lie near the nonreal ones.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"12 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":"114407296","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
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