Linearization Based on Least Squares Approximation with Application to Finite Dimensional System Equations

摘要

The linearization problem is generalized in the sense of approximating nonlinear equations by linear equations within a particular operation region. Least squares linearization methods based on this principle are defined and compared to classical linearization based on truncated Taylor expansion. An analytical evaluation method of least squares linearizations and a numerical method are presented. Applications of linearizations to a simple nonlinear equation demonstrate the possibilities of the method. Application to finite dimensional system equations is described. A modified Newton method based on rudimentary least squares linearization for solving sets of nonlinear equations is discussed.