This paper presents a novel reduced-order algorithm for identifying rational models. From the Arnoldi process, an orthonormal basis of the Krylov subspace is constructed. Based on the Krylov subspace, a high-order cost function is transformed into a low-order one, thereby significantly reducing the computational efforts. This algorithm can be considered as a reduced-order least squares (LS) algorithm or an extension of the traditional gradient iterative (GI) algorithm for different Krylov subspaces, and it presents several advantages over the traditional LS and GI algorithms. The simulated numerical results/figures are consistent with the analytically derived results in terms of the feasibility and effectiveness of the proposed algorithm.

本文提出了一种新颖的降阶算法，用于识别有理模型。通过Arnoldi过程，构造了Krylov子空间的正交基础。基于Krylov子空间，高阶代价函数被转换为低阶代价函数，从而显着减少了计算量。该算法可以被视为降阶最小二乘（LS）算法或针对不同Krylov子空间的传统梯度迭代（GI）算法的扩展，并且与传统的LS和GI算法相比，它具有一些优势。就所提出算法的可行性和有效性而言，模拟的数值结果/数字与分析得出的结果一致。