A Mathematical Characterization of the Performance of the "Multi-Slice" Projector
For researchers in model-order reduction, this provides a theoretical foundation for a new projection method, though the practical gains are not quantified.
The paper mathematically characterizes the performance of a 'multi-slice' projector, an enhanced Petrov-Galerkin method, showing it outperforms the standard approach in certain model-order reduction scenarios.
We consider an enhanced version of the well-kwown "Petrov-Galerkin" projection in Hilbert spaces. The proposed procedure, dubbed "multi-slice" projector, exploits the fact that the sought solution belongs to the intersection of several high-dimensional slices. This setup is for example of interest in model-order reduction where this type of prior may be computed off-line. In this note, we provide a mathematical characterization of the performance achievable by the multi-slice projector and compare the latter with the results holding in the Petrov-Galerkin setup. In particular, we illustrate the superiority of the multi-slice approach in certain situations.