Chapter 1 - General introduction and scope of the book

Abstract

This chapter addresses some preliminary data processing tools that are needed in the remainder of the book. These tools include singular value decomposition in its various versions (economy, compact, and truncated singular value decomposition), proper orthogonal decomposition, and higher order singular value decomposition in its various versions (economy, compact, and truncated higher order singular value decomposition). These tools are illustrated with some toy models. An introduction to reduced order models, both data-driven and projection-based, is also included. The organization of the book is summarized at the end of the chapter. Some selected practice problems are proposed in Annex 1.1. Some MATLAB functions are also given in Annex 1.2 that allow for computing the various versions of singular value decomposition and higher order singular value decomposition.