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Recent results in local convergence and semilocal convergence analysis constitute a natural framework for the theoretical study of iterative methods. This monograph provides a comprehensive study of both basic theory and new results in the area. Each chapter contains new theoretical results and important applications in engineering, modeling dynamic economic systems, inputoutput systems, optimization problems, and nonlinear and linear differential equations. Several classes of operators are considered, including operators without Lipschitz continuous derivatives, operators with high order derivatives, and analytic operators. Each section is selfcontained. Examples are used to illustrate the theory and exercises are included at the end of each chapter. The book assumes a basic background in linear algebra and numerical functional analysis. Graduate students and researchers will find this book useful. It may be used as a selfstudy reference or as a supplementary text for an advanced course in numerical functional analysis.
Convergence  Iterative methods (Mathematics)  NewtonRaphson method  Convergence (Mathématiques)  Itération (Mathématiques)  Convergence.  Iterative methods (Mathematics).  NewtonRaphson method.  Engineering & Applied Sciences  Applied Mathematics  Method, NewtonRaphson  Method of tangents  Newton approximation method  Newton iterative process  Newton method  NewtonRaphson algorithm  NewtonRaphson formula  NewtonRaphson process  Newton's approximation method  Newton's method  Quadratically convergent NewtonRaphson process  Raphson method, Newton  Secondorder NewtonRaphson process  Iteration (Mathematics)  Mathematics.  Functional analysis.  Computer mathematics.  Numerical analysis.  Numerical Analysis.  Computational Mathematics and Numerical Analysis.  Functional Analysis.  Numerical analysis  Functions  Computer science  Functional calculus  Calculus of variations  Functional equations  Integral equations  Computer mathematics  Discrete mathematics  Electronic data processing  Mathematical analysis  Mathematics
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