2017/10/20 by Martin Redmann, Redmann, Martin, Patrick Kürschner +1
Engineering · Mathematics · Physics and Astronomy · #93A15 #93B99 #93C05 #93C15 #93D20 #FOS: Mathematics #Model Reduction and Neural Networks #Numerical methods for differential equations #Optimization and Control (math.OC) #Power System Optimization and Stability
paper · pdf · doi:10.48550/arxiv.1710.07572
openalex publication_date 2017/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When solving partial differential equations numerically, usually a high order spatial discretization is needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized systems and hence reduce computational complexity. A particular MOR technique to obtain a reduced order model (ROM) is balanced truncation (BT). However, if one aims at finding a good ROM on a certain finite time interval only, time-limited BT (TLBT) can be a more accurate alternative. So far, no error bound on TLBT has been proved. In this paper, we close this gap in the theory by providing an \mathcal H2 error bound for TLBT with two different representations. The performance of the error bound is then shown in several numerical experiments.