The iterative rational Krylov algorithm (IRKA) is a commonly used fixed-point iteration developed to minimize the $\mathcal{H}_2$ model order reduction error. In this work, IRKA is recast as a Riemannian gradient descent method with a fixed step size over the manifold of rational functions having fixed degree. This interpretation motivates the development of a Riemannian gradient descent method utilizing as a natural extension variable step size and line search. Comparisons made between IRKA and this extension on a few examples demonstrate significant benefits.

翻译：迭代有理Krylov算法（IRKA）是一种常用的不动点迭代方法，旨在最小化$\mathcal{H}_2$模型降阶误差。本文中，IRKA被重新表述为一种在固定次数的有理函数流形上采用固定步长的黎曼梯度下降方法。这种解释促使我们开发了一种利用可变步长和线搜索作为自然扩展变量的黎曼梯度下降方法。通过几个示例对IRKA及其扩展方法进行的比较，展示了显著的优越性。