Enhanced Error Bounds For The Masked Projection Techniques via Cosine-Sine Decomposition

TL;DR

This paper introduces new, tighter error bounds for masked projection techniques in non-linear model reduction, utilizing cosine-sine decomposition, with specific application to the discrete empirical interpolation method (DEIM).

Contribution

The paper derives generalized error bounds for masked projection techniques using cosine-sine decomposition, improving upon existing bounds and applicable to DEIM.

Findings

Proposed error bounds are tighter than existing ones.

Error bounds are applicable to DEIM in non-linear model reduction.

The bounds are derived using cosine-sine decomposition.

Abstract

The masked projection techniques are popular in the area of non-linear model reduction. Quantifying and minimizing the error in model reduction, particularly from masked projections, is important. The exact error expressions are often infeasible. This leads to the use of error-bound expressions in the literature. In this paper, we derive two generalized error bounds using cosine-sine decomposition for uniquely determined masked projection techniques. Generally, the masked projection technique is employed to efficiently approximate non-linear functions in the model reduction of dynamical systems. The discrete empirical interpolation method (DEIM) is also a masked projection technique; therefore, the proposed error bounds apply to DEIM projection errors. Furthermore, the proposed error bounds are shown tighter than those currently available in the literature.