标题： 双线性迭代有理Krylov算法的稳定性分析 显示英文标题

标题： Stability Analysis of Bilinear Iterative Rational Krylov Algorithm

摘要： 来自不同物理应用的模型规模非常大。 对这些系统进行仿真成本很高，因此通常会通过模型降维得到一个简化模型，该模型能够复制原始完整模型的输入输出行为。 一种最近提出的用于双线性动力系统模型降维的算法，双线性迭代有理Krylov算法（BIRKA），是以局部最优的方式进行的。 该算法需要求解非常大的线性方程组。 通常这些方程组通过直接方法（例如LU分解）求解，这非常昂贵。 更好的选择是使用迭代方法（例如Krylov方法）。 然而，迭代方法在求解线性方程时会引入误差，因为它们不是精确的。 它们会将给定的线性方程组求解到一定的容差范围内。 我们证明，在一些温和的假设下，BIRKA对于不精确线性求解引入的误差是稳定的。 我们还分析了使用这些不精确求解得到的简化系统的准确性，并通过数值实验支持我们的所有结果。 显示英文摘要

摘要： Models coming from different physical applications are very large in size. Simulation with such systems is expensive so one usually obtains a reduced model (by model reduction) that replicates the input-output behaviour of the original full model. A recently proposed algorithm for model reduction of bilinear dynamical systems, Bilinear Iterative Rational Krylov Algorithm (BIRKA), does so in a locally optimal way. This algorithm requires solving very large linear systems of equations. Usually these systems are solved by direct methods (e.g., LU), which are very expensive. A better choice is iterative methods (e.g., Krylov). However, iterative methods introduce errors in linear solves because they are not exact. They solve the given linear system up to a certain tolerance. We prove that under some mild assumptions BIRKA is stable with respect to the error introduced by the inexact linear solves. We also analyze the accuracy of the reduced system obtained from using these inexact solves and support all our results by numerical experiments.