The most commonly used solutions methods are iterative, when starting from one or several initial approximations a sequence is constructed, which converges to a solution of the equation. Iteration methods are applied also for solving optimization problems. In such cases the iteration sequences converge to an optimal solution of the problem at hand. Since all of these methods have the same recursive structure, they can be introduced and discussed in a general framework. This book examines new results that find applications in engineering, in dynamic economic systems, in input-output systems, in the solution of nonlinear and linear differential equations and optimization problems.