A Mathematical Characterization of the Performance of the "Multi-Slice" Projector

TL;DR

This paper introduces a 'multi-slice' projector, an advanced projection method in Hilbert spaces that leverages multiple high-dimensional slices to improve performance over traditional Petrov-Galerkin methods, especially in model-order reduction.

Contribution

It provides a mathematical analysis of the multi-slice projector and demonstrates its advantages over Petrov-Galerkin in specific scenarios.

Findings

Multi-slice projector outperforms Petrov-Galerkin in certain cases.

Mathematical characterization of the multi-slice method's performance.

Potential applications in model-order reduction.

Abstract

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.