检索结果-内蒙古大学图书馆

linear-time CUR approximation of BEM matrices

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2020年 368卷 112528-000页

作者： Ayala, Alan Claeys, Xavier Grigori, Laura Univ Paris Diderot SPC Sorbonne Univ INRIA Paris CNRSLab Jacques Louis LionsEquipe ALPINES Paris France Univ Paris Diderot SPC Sorbonne Univ CNRS INRIALab Jacques Louis LionsEquipe ALPINES F-75005 Paris France

In this paper we propose linear-time CUR approximation algorithms for admissible matrices obtained from the hierarchical form of Boundary Element matrices. We propose a new approach called geometric sampling to obtain indices of most significant rows and columns using information from the domains where the problem is posed. Our strategy is tailored to Boundary Element Methods (BEM) since it uses directly and explicitly the cluster tree containing information from the problem geometry. Our CUR algorithm has precision comparable with low-rank approximations created with the truncated QR factorization with column pivoting (QRCP) and the Adaptive Cross Approximation (ACA) with full pivoting, which are quadratic-cost methods. When compared to the well-known linear-time algorithm ACA with partial pivoting, we show that our algorithm improves, in general, the convergence error and overcomes some cases where ACA fails. We provide a general relative error bound for CUR approximations created with geometrical sampling. Finally, we evaluate the performance of our algorithms on traditional BEM problems defined over different geometries. (C) 2019 Elsevier B.V. All rights reserved.

关键词： CUR approximation linear time algorithms BEM matrices

来源：评论

学校读者我要写书评

暂无评论

DECAY BOUNDS AND O(n) algorithms FOR APPROXIMATING FUNCTIONS OF SPARSE MATRICES

引用

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS 2007年 28卷 16-39页

作者： Benzi, Michele Razouk, Nader Emory Univ Dept Math & Comp Sci Atlanta GA 30322 USA

We establish decay bounds for the entries of f(A), where A is a sparse (in particular, banded) n x n diagonalizable matrix and f is smooth on a subset of the complex plane containing the spectrum of A. Combined with techniques from approximation theory, the bounds are used to compute sparse (or banded) approximations to f(A), resulting in algorithms that under appropriate conditions have linear complexity in the matrix dimension. Applications to various types of problems are discussed and illustrated by numerical examples.

关键词： Matrix functions sparse and banded matrices decay rates linear time algorithms Chebyshev polynomials Faber polynomials density matrix trace determinant

来源：评论

学校读者我要写书评

暂无评论

linear structure of bipartite permutation graphs and the longest path problem

引用

INFORMATION PROCESSING LETTERS 2007年第2期103卷 71-77页

作者： Uehara, Ryuhei Valiente, Gabriel JAIST Sch Informat Sci Ishikawa 9231292 Japan Tech Univ Catalonia Dept Software E-08034 Barcelona Spain

The class of bipartite permutation graphs is the intersection of two well known graph classes: bipartite graphs and permutation graphs. A complete bipartite decomposition of a bipartite permutation graph is proposed in this note. The decomposition gives a linear structure of bipartite permutation graphs, and it can be obtained in O(n) time, where n is the number of vertices. As an application of the decomposition, we show an O(n) time and space algorithm for finding a longest path in a bipartite permutation graph. (C) 2007 Elsevier B.V. All rights reserved.

关键词： bipartite permutation graphs graph decomposition linear time algorithms graph algorithms

来源：评论

学校读者我要写书评

暂无评论

Reasoning with minimal models: efficient algorithms and applications

引用

ARTIFICIAL INTELLIGENCE 1997年第2期96卷 421-449页

作者： Ben-Eliyahu-Zohary, R Palopoli, L Ben Gurion Univ Negev Dept Math & Comp Sci IL-84105 Beer Sheva Israel Univ Calabria DEIS I-87030 Arcavacata Di Rende CS Italy

Reasoning with minimal models is at the heart of many knowledge-representation systems. Yet it turns out that this task is formidable, even when very simple theories are considered. In this paper, we introduce the elimination algorithm, which performs, in linear time, minimal model finding and minimal model checking for a significant subclass of positive CNF theories which we call positive bead-cycle-free (HCF) theories. We also prove that the task of minimal entailment is easier for positive HCF theories than it is for the class of all positive CNF theories. Finally, we show how variations of the elimination algorithm can be applied to allow queries posed on disjunctive deductive databases and disjunctive default theories to be answered in an efficient way. (C) 1997 Published by Elsevier Science B.V.

关键词： minimal models disjunctive databases disjunctive default logic disjunctive logic programs stable model semantics linear time algorithms

来源：评论

学校读者我要写书评

暂无评论

linear algorithms for preemptive scheduling of multiprocessor tasks subject to minimal lateness

引用

DISCRETE APPLIED MATHEMATICS 1997年第1-2期72卷 25-46页

作者： Bianco, L Blazewicz, J DellOlmo, P Drozdowski, M INST INFORMAT POLITECH POZNANSKIEJ POZNANPOLAND CNR IST ANAL SISTEMI & INFORMATI-00185 ROMEITALY POLISH ACAD SCI INST INFORMAT TEORETYCZNEJ & STOSOWANEJGLIWICEPOLAND

In scheduling theory it is widely assumed that a task is to be processed on one processor at a time. This assumption is not so obvious in the context of recently emerging parallel computer systems and parallel algorithms. In this work we consider tasks requiring more than one dedicated processor at a time, i.e. sets of processors simultaneously. linear time algorithms will be given for the case of two, three and four processors and the L(max) criterion. The algorithms are based on the same simple paradigm. In some cases they deliver optimal solutions. In other cases, optimality is not guaranteed but they can still be used as fast approximation algorithms for which the worst case performance bounds are given. Results of the computational experiments involving four processors are reported.

关键词： parallel processing multiprocessor tasks scheduling linear time algorithms

来源：评论

学校读者我要写书评

暂无评论

algorithms for a class of isotonic regression problems

引用

ALGORITHMICA 1999年第3期23卷 211-222页

作者： Pardalos, PM Xue, G Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA Univ Vermont Dept Comp Sci Burlington VT 05405 USA

The isotonic regression problem has applications in statistics, operations research, and image processing. In this paper a general framework for the isotonic regression algorithm is proposed. Under this framework, we discuss the isotonic regression problem in the case where the directed graph specifying the order restriction is a directed tree with n vertices. A new algorithm is presented for this case, which can be regarded as a generalization of the PAV algorithm of Ayer et al. Using a simple tree structure such as the binomial heap, the algorithm can be implemented in O(n log n) time, improving the previously best known O(n(2)) time algorithm. We also present linear time algorithms for special cases where the directed graph is a path or a star.

关键词： isotonic regression binomial heap linear time algorithms

来源：评论

学校读者我要写书评

暂无评论

Improved approximation algorithms for embedding hyperedges in a cycle

引用

INFORMATION PROCESSING LETTERS 1998年第5期67卷 267-271页

作者： Gonzalez, TE Univ Calif Santa Barbara Dept Comp Sci Santa Barbara CA 93106 USA

Approximation algorithms for embedding hyperedges in a cycle so as to minimize the maximum congestion are presented. Our algorithms generate an embedding by transforming the problem into another problem solvable in polynomial time. One algorithm transforms it to a linear programming problem, and the other one to the problem of embedding edges in a cycle. Both algorithms generate an embedding with congestion at most twice of that in an optimal solution. Our problem has applications in CAD and parallel computation. (C) 1998 Elsevier Science B.V. All rights reserved.

关键词： approximation algorithms parallel computation CAD linear time algorithms minimize congestion

来源：评论

学校读者我要写书评

暂无评论

An algebraic metric for phylogenetic trees

引用

APPLIED MATHEMATICS LETTERS 2009年第9期22卷 1320-1324页

作者： Alberich, Ricardo Cardona, Gabriel Rossello, Francesc Valiente, Gabriel Univ Balearic Isl Dept Math & Comp Sci E-07122 Palma de Mallorca Spain Tech Univ Catolonia Dept Software E-08034 Barcelona Spain

The definition of similarity measures for phylogenetic trees has been motivated by the computation of consensus trees, the search by similarity in databases, and the assessment of phylogenetic reconstruction methods. The transposition distance for fully resolved trees is a recent addition to the extensive collection of available metrics for comparing phylogenetic trees. In this work, we generalize the transposition metric from fully resolved to arbitrary phylogenetic trees, through a construction that involves an embedding of the set of phylogenetic trees (up to isomorphisms) with a fixed number of labeled leaves into a symmetric group. We also show that this transposition distance can be computed in linear time and we establish some of its basic properties. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Phylogenetic trees Metric Distance Permutations linear time algorithms

来源：评论

学校读者我要写书评

暂无评论

An O(n) algorithm for weighted least squares regression by integer quasi-convex and unimodal or umbrella functions

引用

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2009年第4期58卷 776-783页

作者： Liu, Ming-Hong Ubhaya, Vasant A. N Dakota State Univ Dept Comp Sci & Operat Res Dept 2740 Fargo ND 58108 USA Teradata Inc Miamisburg OH 45342 USA

The problem of fitting n data points by an integer quasi-convex (also quasi-concave, umbrella or unimodal) function using the weighted least squares distance function is considered. An algorithm of linear time (O(n)) worst-case complexity and thus optimal is constructed for computing a best fit. This problem arises in the context of curve fitting or statistical estimation. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Least squares regression Integer quasi-convex regression Integer unimodal regression Integer umbrella regression Umbrella ordering Isotonic regression linear time algorithms Greatest convex minorant (GCM) Least concave majorant (LCM)

来源：评论

学校读者我要写书评

暂无评论

Digital topological method for computing genus and the Betti numbers

引用

TOPOLOGY AND ITS APPLICATIONS 2010年第12期157卷 1931-1936页

作者： Chen, Li Rong, Yongwu George Washington Univ Washington DC 20052 USA

This paper concerns with computation of topological invariants such as genus and the Betti numbers. We design a linear time algorithm that determines such invariants for digital spaces in 3D. These computations could have applications in medical imaging as they can be used to identify patterns in 3D image. Our method is based on cubical images with direct adjacency, also called (6, 26)-connectivity images in discrete geometry. There are only six types of local surface points in such a digital surface. Two mathematical ingredients are used. First, we use the Gauss-Bonnett Theorem in differential geometry to determine the genus of 2-dimensional digital surfaces. This is done by counting the contribution for each of the six types of local surface points. The new formula derived in this paper that calculates genus is g = 1 + (vertical bar M-5 vertical bar + 2 . vertical bar M-6 vertical bar - vertical bar M-3 vertical bar)/8 where M-i indicates the set of surface-points each of which has i adjacent points on the surface. Second, we apply the Alexander duality to express the homology groups of a 3D manifold in the usual 3D space in terms of the homology groups of its boundary surface. While our result is stated for digital spaces, the same idea can be applied to simplicial complexes in 3D or more general cell complexes. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Digital surface points Genus Betti numbers Gauss-Bonnett theorem linear time algorithms

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：