Looking for the order of a system of arbitrary ordinary differential equations
Looking for the order of a system of arbitrary ordinary differential equations
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DOI：
10.1007/s00200-009-0087-3
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发表时间：
2009-04
期刊：
影响因子：
--
通讯作者：
F. Ollivier
中科院分区：
文献类型：
--
作者：
F. Ollivier
本文由S. Cohn和C. W. Borchardt从C. G. J·雅可比考虑了给定系统常微分方程可能采用的各种标准形式。在不使用规范形式的情况下寻找系统的阶数，就归结为一个不等式问题：做作问题。本文介绍了一种新的计算公式--截尾行列式。这个量的非零性意味着阶数将等于这个不等式问题的解H，它是通过类似于Harold Kuhn的匈牙利方法的算法获得的。
This paper was edited by S. Cohn and C. W. Borchardt from posthumous manuscripts of C. G. J. Jacobi. The various canonical forms that a given system ordinary differential equations may take are considered. Looking for the order of the system, without using a normal form, is reduced to a problem of inequalities: theaffectation problem. A new type of formulas, the truncated determinants, is introduced. The non vanishing of this quantity means that the order will be equal to the valueH, solution of this inequalities problem, which is obtained by an algorithm similar to Harold Kuhn’s Hungarian method.