论文标题
带有虚拟杆信息同化的Padé矩阵铅笔法
The Padé matrix pencil method with spurious pole information assimilation
论文作者
论文摘要
我们提出了一种用于计算帕德近近似值的新方法，该方法能够消除在发育点上放置的伪造杆，并通过精确限制和/或噪声系数识别和消除伪造和消除杂波。消除极点中包含的信息被吸收，产生降低的订单板大约（PA）。尽管该算法产生的[M+K/M]构象是灵活的，但此处报道的算法产生的有理近似值的M值取决于消除的杂波杆的数量。由于系数噪声/精度限制引起的伪造杆，使用循证滤波器参数应用于由串联系数组成的矩阵的奇异值。通过求解由基质铅笔定义的广义特征值问题直接找到合理函数极。伪造的波雷斯位于发展时期的某些算法中，其幅度确定了。通过求解过度确定的线性基质方程来找到残基。将该方法与所谓的健壮帕德近似（RPA）方法进行了比较，并证明在研究的问题上具有竞争力。通过消除伪造杆，尤其是在具有分支点的功能中，例如遇到的解决功率流问题的函数，可以使这些复杂评估问题的解决方案更加可靠。
We present a novel method for calculating Padé approximants that is capable of eliminating spurious poles placed at the point of development and of identifying and eliminating spurious poles created by precision limitations and/or noisy coefficients. Information contained in in the eliminated poles is assimilated producing a reduced order Padé approximant (PA). While the [m+k/m] conformation produced by the algorithm is flexible, the m value of the rational approximant produced by the algorithm reported here is determined by the number of spurious poles eliminated. Spurious poles due to coefficient noise/precision limitations are identified using an evidence-based filter parameter applied to the singular values of a matrix comprised of the series coefficients. The rational function poles are found directly by solving a generalized eigenvalue problem defined by a matrix pencil. Spurious poles place at the point of development, responsible in some algorithms for degeneracy, are identified by their magnitudes. Residues are found by solving an overdetermined linear matrix equation. The method is compared with the so-called Robust Padé Approximation (RPA) method and shown to be competitive on the problems studied. By eliminating spurious poles, particularly in functions with branch points, such as those encountered solving the power-flow problem, solution of these complex-valued problems is made more reliable.
