An alternative linearization technique

Abstract

The numerical treatment of non‐linear engineering phenomena often involves some sort of mathematical simplification. In many cases, the system under investigation is linearized about an operating point using the linear part of the Taylor’s series expansion. This allows local representation for use in incremental or iterative methods using well‐established computational tools for linear algebra. Demonstrates a different linearization technique that generally provides a higher quality fit to a certain class of functions than the standard Taylor linearization. This class of functions is general enough to represent all systems of algebraic equations. Presents a graphical demonstration of the quality of fit along with a discussion of why this alternative linearization provides a high quality fit. Also presents an engineering application of the linearization.