通过行和列计算稀疏雅可比矩阵

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 1998-01-01 DOI:10.1080/10556789808805700

A. Hossain, T. Steihaug

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引用次数: 45

摘要

大型稀疏雅可比矩阵的有效估计问题近年来得到了广泛的研究。我们已经注意到，雅可比矩阵的估计可以被看作是一个图的着色问题。矩阵的元素通过在与一组结构独立的列相对应的几个方向上取除差来估计。另一种可能性是通过所谓的自动微分来获得非零元素，这种方法给出的估计没有在分差格式中遇到的截断误差。在本文中，我们证明了利用自动微分的正向和反向模式来利用列和行中的稀疏性是可能的。给出了该问题的图论刻画。

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Computing a sparse Jacobian matrix by rows and columns

Efficient estimation of large sparse Jacobian matrices has been studied extensively in the last couple of years. It has been observed that the estimation of Jacobian matrix can be posed as a graph coloring problem. Elements of the matrix are estimated by taking divided difference in several directions corresponding to a group of structurally independent columns. Another possibility is to obtain the nonzero elements by means of the so called Automatic differentiation, which gives the estimates free of truncation error that one encounters in a divided difference scheme. In this paper we show that it is possible to exploit sparsity both in columns and rows by employing the forward and the reverse mode of Automatic differentiation. A graph-theoretic characterization of the problem is given.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.