Fast H2-optimal model order reduction exploiting the local nature of Krylov-subspace methods
Fast H2-optimal model order reduction exploiting the local nature of Krylov-subspace methods
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DOI：
10.1109/ecc.2016.7810578
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发表时间：
2016-06
期刊：
影响因子：
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通讯作者：
A. Castagnotto;H. Panzer;B. Lohmann
中科院分区：
文献类型：
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作者：
A. Castagnotto;H. Panzer;B. Lohmann
有理Krylov子空间方法是一个注定的候选人在减少非常大规模的线性模型，由于其适度的计算成本和内存需求。然而，为了实现良好的近似结果，最先进的Krylov算法，如IRKA迭代搜索一组局部H2最优约简参数。这种搜索需要反复减少的高维模型，因此仍然可以占显着的计算成本，特别是在缓慢收敛的情况下。在这篇文章中，我们研究了H2-最优理性Krylov方法的成本，并提出了一个增强的减少框架，基于这种方法的局部性质，以减少计算工作量，同时保证收敛时的最优性。通过这个框架实现的改进进行了理论分析和数值验证上修改的IRKA算法。
Rational Krylov-subspace methods are a predestined candidate in the reduction of very-large-scale linear models due to their moderate computational cost and memory requirements. However, in order to achieve good approximation results, state-of-the-art Krylov algorithms like IRKA iteratively search for a set of locally H2-optimal reduction parameters. This search requires the repeated reduction of the high-dimensional model and can therefore still account for significant computational cost, especially in case of slow convergence. In this contribution, we investigate the cost of H2-optimal rational Krylov methods and propose an enhanced reduction framework, based on the local nature of such methods, to reduce the computational effort while guaranteeing optimality at convergence. The improvement achieved through this framework is analyzed theoretically and validated numerically on a modified IRKA algorithm.