Optimal Monomial Quadratization for ODE Systems
Optimal Monomial Quadratization for ODE Systems
复制标题
ODE 系统的最优单项式二次化
DOI：
10.1007/978-3-030-79987-8_9
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Pogudin, Gleb
中科院分区：
文献类型：
--
作者：
Bychkov, Andrey;Pogudin, Gleb
将多项式常微分方程系统转化为特殊的二次型已被成功地用作模型降阶方法的预处理步骤。然而，据我们所知，一直没有实际的算法自动执行这一步骤的任何最优性guarantees.We提出了一个算法，给定一个系统的多项式ODE，发现一个转换成二次ODE系统通过引入新的变量是单项式的原始变量。该算法保证产生这种形式的最佳变换。该算法的实现，我们证明它的例子从文献。
Transformation of a polynomial ODE system to a special quadratic form has been successfully used recently as a preprocessing step for model order reduction methods. However, to the best of our knowledge, there has been no practical algorithm for performing this step automatically with any optimality guarantees.We present an algorithm that, given a system of polynomial ODEs, finds a transformation into a quadratic ODE system by introducing new variables which are monomials of the original variables. The algorithm is guaranteed to produce an optimal transformation of this form. The algorithm is implemented, and we demonstrate it on examples from the literature.