Iterative Solution of Equations; Convergence of Sequences

Abstract

In this chapter, we are concerned with the problem of solving an equation of the form

$$f(x) = 0$$

((2.1))

. The basic principle of our methods is to generate a sequence of estimates of the required solution which we hope converges to this solution. It will therefore be necessary to study exactly what is meant by these terms and this is done later in this chapter. A much fuller treatment of the convergence of sequences has been given by Hawkins (1988).