English

An $\mathcal H_2$-Type Error Bound for Time-Limited Balanced Truncation

Optimization and Control 2017-10-23 v1

Abstract

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\mathcal H_2 error bound for TLBT with two different representations. The performance of the error bound is then shown in several numerical experiments.

Cite

@article{arxiv.1710.07572,
  title  = {An $\mathcal H_2$-Type Error Bound for Time-Limited Balanced Truncation},
  author = {Martin Redmann and Patrick Kürschner},
  journal= {arXiv preprint arXiv:1710.07572},
  year   = {2017}
}
R2 v1 2026-06-22T22:20:35.060Z