This self-contained treatment offers a contemporary and systematic development of the theory and application of Newton methods, which are undoubtedly the most effective tools for solving equations appearing in computational sciences. Its focal point resides in an exhaustive analysis of the convergence properties of several Newton variants used in connection to specific real life problems originated from astrophysics, engineering, mathematical economics and other applied areas. What distinguishes this book from others is the fact that the weak convergence conditions inaugurated here allow for...

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 optimisation 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,...