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Markowitz-Type Heuristics for Computing Jacobian Matrices Efficiently

机译:Markowitz型启发式算法可有效计算Jacobian矩阵

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摘要

We consider the problem of accumulating the Jacobian matrix of a nonlinear vector function by using a minimal number of arithmetic operations. Two new Markowitz-type heuristics are proposed for vertex elimination in linearized computational graphs, and their superiority over existing approaches is shown by several tests. Similar ideas are applied to derive new heuristics for edge elimination techniques. The well known superiority of edge over vertex elimination can be observed only partially for the heuristics discussed in this paper. Nevertheless, significant improvements can be achieved by the new heuristics both in terms of the quality of the results and their robustness with respect to different tiebreaking criteria.
机译:我们考虑通过使用最少数量的算术运算来累积非线性矢量函数的雅可比矩阵的问题。提出了两种新的Markowitz型启发式方法来消除线性化计算图中的顶点,并通过几次测试证明了它们在现有方法上的优越性。相似的思想被应用于为边缘消除技术推导新的启发式方法。对于本文讨论的启发式方法,只能部分地观察到边缘优于顶点消除的众所周知的优势。但是,通过新的启发式方法,无论是结果的质量还是针对不同决胜标准的稳健性,都可以实现重大改进。

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