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

A Contemporary Study of Iterative Methods evaluates and compares advances in iterative techniques, and their numerous applications in applied mathematics, engineering, mathematical economics, mathematical biology, and other applied sciences. Oftentimes, dynamic systems are modeled by difference or differential equations, and their solutions represent the states of the systems. Similar equations are also used in the case of discrete systems. The 'unknowns' of engineering equations can be functions (difference, differential, and integral equations), vectors, (systems of linear and nonlinear algebraic equations), or real or complex numbers (single algebraic equations with single unknowns). Except in special cases, the most commonly used solution methods are iterative - when starting from one or several approximations a sequence is constructed that converges to a solution of the equation. 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. Since all these methods have the same recursive structure, they can be introduced and discussed in a general framework. Contains recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces, and present several applications and connections with fixed point theoryEncompasses the novel tool of dynamic analysis for iterative methods, including new developments in Smale stability theory and polynomiographyExplores the uses of computation of iterative methods across nonlinear analysis, placing the useful technique before non-specialist users from many application fieldsUniquely places discussion of derivative-free methods in context of other discoveries, aiding comparison and contrast between options INDICE: The majorization method in the Kantorovich theoryDirectional Newton methods Newton's method Generalized equations Gauss-Newton method Gauss-Newton method for convex optimization Proximal Gauss-Newton method MMN-HSS method Secant-like methods in chemistry Robust convergence of Newton's method for cone inclusion problem Gauss-Newton method for convex composite optimization Domain of parameters Newton's method for solving optimal shape design problems Osada method Newton method to solve equations with solutions of multiplicity greater than one Laguerre-like method for multiple zeros 1Traub's method for multiple roots Extended application of the shadowing lemma for operators with chaotic behaviourIntroduction to dynamicsInexact two-point Newton-like methodsTwo-setp Newton methodsConvergence and the dynamics of Chebyshev-Halley type methodsConvergence plances of iterative methodsConvergence and dynamics of an optimal fourth-order familyConvergence and dynamics of three-step iterative methods for multiple zeros

• ISBN: 978-0-12-809214-9
• Editorial: Academic Press
• Encuadernacion: Rústica
• Páginas: 400
• Fecha Publicación: 01/03/2018
• Nº Volúmenes: 1
• Idioma: Inglés