Mathematical Principles Related to Modern System Analysis

In the mathematical field of numerical analysis, model order reduction is the key to processing measured data. This chapter outlines philosophy of model order reduction along with the concepts of total least squares and singular value decomposition. It introduces a critical component in solving a total least squares problem called the singular value decomposition. The singular value decomposition is one of the most important concepts in linear algebra. Eigenvectors and eigenvalues play crucial roles in linear algebra ranging from simplifying matrix algebra such as taking the 500th power of to solving differential equations. Diagonalizing a matrix not only provides a quick way to extract eigenvalues but important parameters such as the rank and dimension of a matrix can be found easily once a matrix is diagonalized. The method of total least squares is a linear parameter estimation technique and is used in wide variety of disciplines such as signal processing, statistics, physics, and the like.