Accelerating convergence of iterative processes

A technique is discussed which, when applied to an iterative procedure for the solution of an equation, accelerates the rate of convergence if the iteration converges and induces convergence if the iteration diverges. An illustrative example is given. 1. Introduction This paper discusses a technique for accelerating the convergence of iterative procedures employed in the solution of non-linear algebraic and transcendental equations. Iterative procedures in problems of this kind are of considerable importance since, with the aid of high speed computers, they very often provide the only effective means of solving such equations. The methods described here are of interest because they are capable of producing solutions even in those cases where the iteration algorithm may be divergent.