The derivations of existing error bounds for reduced order models of time varying partial
differential equations (PDEs) constructed using proper orthogonal decomposition (POD) …

In this paper, we resolve several long-standing issues dealing with optimal pointwise in time
error bounds for proper orthogonal decomposition (POD) reduced order modeling of the …

We propose an incremental algorithm to compute the proper orthogonal decomposition
(POD) of simulation data for a partial differential equation. Specifically, we modify an …

This paper introduces a novel framework for the solution of (large-scale) Lyapunov and
Sylvester equations derived from numerical integration methods. Suitable systems of …

In our previous work [JR Singler, SIAM J. Numer. Anal., 52 (2014), pp. 852--876], we
considered the proper orthogonal decomposition (POD) of time varying PDE solution data …

In a recent work (Koc et al., SIAM J. Numer. Anal. 59 (4), 2163–2196,), the authors showed
that including difference quotients (DQs) is necessary in order to prove optimal pointwise in …

We give an algorithmic approach to the approximative solution of operator Lyapunov
equations for controllability. Motivated by the successfully applied alternating direction …

In our earlier work Fareed et al.(2018)[18], we developed an incremental approach to
compute the proper orthogonal decomposition (POD) of PDE simulation data. Specifically …

We consider convergence analysis for a model reduction algorithm for a class of linear
infinite dimensional systems. The algorithm computes an approximate balanced truncation …

The solution of large-scale matrix algebraic Riccati equations is important for instance in
control design and model reduction and remains an active area of research. We consider a …