WIAS Preprint No. 2440, (2017)

An $H_2$-type error bound for time-limited balanced truncation


  • Redmann, Martin
    ORCID: 0000-0001-5182-9773
  • Kürschner, Patrick

2010 Mathematics Subject Classification

  • 93A15 93B99 93C05


  • Model reduction, linear systems, time-limited balanced truncation, time-limited Gramians, error bound




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 H2 error bound for TLBT with two different representations. The performance of the error bound is then shown in several numerical experiments

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