Computing a sparse Jacobian matrix by rows and columns

IF 1.4 3区数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Optimization Methods & Software Pub Date : 1998-01-01 DOI:10.1080/10556789808805700

A. Hossain, T. Steihaug

引用次数: 45

Abstract

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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通过行和列计算稀疏雅可比矩阵

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Optimization Methods & Software 工程技术-计算机：软件工程

CiteScore

4.50

自引率

0.00%

发文量

审稿时长

7 months

期刊介绍： Optimization Methods and Software publishes refereed papers on the latest developments in the theory and realization of optimization methods, with particular emphasis on the interface between software development and algorithm design. Topics include: Theory, implementation and performance evaluation of algorithms and computer codes for linear, nonlinear, discrete, stochastic optimization and optimal control. This includes in particular conic, semi-definite, mixed integer, network, non-smooth, multi-objective and global optimization by deterministic or nondeterministic algorithms. Algorithms and software for complementarity, variational inequalities and equilibrium problems, and also for solving inverse problems, systems of nonlinear equations and the numerical study of parameter dependent operators. Various aspects of efficient and user-friendly implementations: e.g. automatic differentiation, massively parallel optimization, distributed computing, on-line algorithms, error sensitivity and validity analysis, problem scaling, stopping criteria and symbolic numeric interfaces. Theoretical studies with clear potential for applications and successful applications of specially adapted optimization methods and software to fields like engineering, machine learning, data mining, economics, finance, biology, or medicine. These submissions should not consist solely of the straightforward use of standard optimization techniques.