A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications

Evaluates and compares advances in iterative techniques, also discussing their numerous applications in applied mathematics, engineering, mathematical economics, mathematical biology and other applied sciences. It uses the popular iteration technique in generating the approximate solutions of complex nonlinear equations that is suitable for aiding in the solution of advanced problems in engineering, mathematical economics, mathematical biology and other applied sciences. Iteration methods are also applied for solving optimization problems. In such cases, the iteration sequences converge to an optimal solution of the problem at hand.

- Contains recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces

- Encompasses the novel tool of dynamic analysis for iterative methods, including new developments in Smale stability theory and polynomiography

- Explores the uses of computation of iterative methods across non-linear analysis

- Uniquely places discussion of derivative-free methods in context of other discoveries, aiding comparison and contrast between options