Techniques of numerical mathematics are often used in statistics, e.g., r oot finding and optimization (minimization or maximization) in maximum likelihood, where analytical methods usually cannot be used because closed form solutions do not exist. This chapter explains the principles of some important numerical methods and their usage.
Sections 7.2 and 7.3 describe methods for solving nonlinear equations and their systems. One can also learn the basic facts about iterative methods and their termination here. Sections 7.4 and 7.5 are dedicated to methods of local unconstrained optimization for uni- and multivariate functions, respectively. Section 7.6 deals with numerical evaluation of function derivatives which is very often used in optimization methods.