Optimal accumulation of Jacobian matrices by elimination methods on the dual computational graph
Optimal accumulation of Jacobian matrices by elimination methods on the dual computational graph
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DOI：
10.1007/s10107-003-0456-9
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发表时间：
2004-04
影响因子：
2.7
通讯作者：
U. Naumann
中科院分区：
文献类型：
--
作者：
U. Naumann
向量函数雅可比矩阵F '的累加 可以看作是它的线性化计算图到有向完全二部图Kn，m的一个子图的变换。这种转换可以通过应用不同的消除技术来执行，这些技术可能导致计算F '的成本变化。本文介绍了面消除的基本技术积累雅可比矩阵，通过使用最少数量的算术运算。它的优势，边和顶点消除方法。其目的是建立的概念基础，为正在进行的开发算法，优化雅可比矩阵的计算。
The accumulation of the Jacobian matrixF’of a vector function can be regarded as a transformation of its linearized computational graph into a subgraph of the directed complete bipartite graphKn,m. This transformation can be performed by applying different elimination techniques that may lead to varying costs for computingF’. This paper introduces face elimination as the basic technique for accumulating Jacobian matrices by using a minimal number of arithmetic operations. Its superiority over both edge and vertex elimination methods is shown. The intention is to establish the conceptual basis for the ongoing development of algorithms for optimizing the computation of Jacobian matrices.