ABSTRACT
This chapter introduces the fundamentals of the theory of general iteration algorithms. The convergence of such algorithmic models is examined under very general conditions. The chapter discusses the main reason that only single-step iteration methods in most publications, because any result on single-step processes automatically applies to multistep processes. The methods discussed are used for solving nonlinear equations and systems of nonlinear equations. The optimization problem of each step may depend on the solutions of very early steps. Multistep processes are also used in many other fields of applied mathematics. The problem of finding the percentiles of a probability distribution can also be reduced to the solution of a nonlinear equation. In constructing confidence intervals the smallest intervals with given probabilities are usually selected. The chapter focuses on that linear equations have numerous applications in engineering and in economy.
