TY - BOOK ID - 5454199 TI - Convergence and Applications of Newton-type Iterations PY - 2008 SN - 9780387727417 0387727418 9780387727431 1441924922 9786611491727 1281491721 0387727434 PB - New York, NY : Springer New York : Imprint: Springer, DB - UniCat KW - Convergence KW - Iterative methods (Mathematics) KW - Newton-Raphson method KW - Convergence (Mathématiques) KW - Itération (Mathématiques) KW - Convergence. KW - Iterative methods (Mathematics). KW - Newton-Raphson method. KW - Engineering & Applied Sciences KW - Applied Mathematics KW - Method, Newton-Raphson KW - Method of tangents KW - Newton approximation method KW - Newton iterative process KW - Newton method KW - Newton-Raphson algorithm KW - Newton-Raphson formula KW - Newton-Raphson process KW - Newton's approximation method KW - Newton's method KW - Quadratically convergent Newton-Raphson process KW - Raphson method, Newton KW - -Second-order Newton-Raphson process KW - Iteration (Mathematics) KW - Mathematics. KW - Functional analysis. KW - Computer mathematics. KW - Numerical analysis. KW - Numerical Analysis. KW - Computational Mathematics and Numerical Analysis. KW - Functional Analysis. KW - Numerical analysis KW - Functions KW - Computer science KW - Functional calculus KW - Calculus of variations KW - Functional equations KW - Integral equations KW - Computer mathematics KW - Discrete mathematics KW - Electronic data processing KW - Mathematical analysis KW - Mathematics UR - https://www.unicat.be/uniCat?func=search&query=sysid:5454199 AB - Recent results in local convergence and semi-local 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, input-output 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 self-contained. 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 self-study reference or as a supplementary text for an advanced course in numerical functional analysis. ER -