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The aim of this monograph is to give a unified introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. It summarizes the most significant contributions in the area by presenting, for each iterative method considered (Picard iteration, Krasnoselskij iteration, Mann iteration, Ishikawa iteration etc.), some of the most relevant, interesting, representative and actual convergence theorems. Applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods, are also presented. Due to the explosive number of research papers on the topic (in the last 15 years only, more than one thousand articles related to the subject were published), it was felt that such a monograph was imperatively necessary. The volume is useful for authors, editors, and reviewers. It introduces concrete criteria for evaluating and judging the plethora of published papers.

Fixed point theory. --- Iterative methods (Mathematics) --- Fixed point theory --- Théorème du point fixe --- Itération (Mathématiques) --- Bibliography. --- Mathematical Theory --- Calculus --- Applied Mathematics --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Iteration (Mathematics) --- Fixed point theorems (Topology) --- Mathematics. --- Operator theory. --- Numerical analysis. --- Topology. --- Operator Theory. --- Numerical Analysis. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Mathematical analysis --- Functional analysis --- Math --- Science --- Numerical analysis --- Nonlinear operators --- Coincidence theory (Mathematics)

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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.

Convergence --- Iterative methods (Mathematics) --- Newton-Raphson method --- Convergence (Mathématiques) --- Itération (Mathématiques) --- Convergence. --- Iterative methods (Mathematics). --- Newton-Raphson method. --- Engineering & Applied Sciences --- Applied Mathematics --- Method, Newton-Raphson --- Method of tangents --- Newton approximation method --- Newton iterative process --- Newton method --- Newton-Raphson algorithm --- Newton-Raphson formula --- Newton-Raphson process --- Newton's approximation method --- Newton's method --- Quadratically convergent Newton-Raphson process --- Raphson method, Newton --- -Second-order Newton-Raphson 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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Classical Circuit Theory provides readers with the fundamental, analytic properties of linear circuits that are important to the design of conventional and non-conventional circuits in modern communication systems. These properties include the relations between phase and gain, between the real and imaginary parts, and between phase and group delay. They also include the fundamental limitations on gain and bandwidth, which are important in broadband matching in amplifier design. The idea that an impedance function is a positive real function and that a transfer function is bounded-real, forms the basis for analytic design of all conventional filters. At the same time, mathematical programming tools are now widely available so that design of non-conventional circuits by optimization is but a few mouse clicks away. Every new concept within the material is illustrated with one or more examples. There are exercises and problems at the end of the chapters. Some may be suitable for term projects. The design techniques presented are also illustrated step by step with easy-to-follow examples.

Electric circuit analysis. --- Electric circuits, Linear --- Design and construction. --- Mathematics. --- Linear electric circuits --- Circuit analysis, Electric --- Electric circuits --- Electric network analysis --- Numerical analysis --- Congresses. --- Systems engineering. --- Electronics. --- Circuits and Systems. --- Electronics and Microelectronics, Instrumentation. --- Engineering systems --- System engineering --- Engineering --- Industrial engineering --- System analysis --- Electrical engineering --- Physical sciences --- Design and construction --- Electronic circuits. --- Microelectronics. --- Microminiature electronic equipment --- Microminiaturization (Electronics) --- Electronics --- Microtechnology --- Semiconductors --- Miniature electronic equipment --- Electron-tube circuits --- Electron tubes --- Iterative methods (Mathematics) --- Analyse numérique. --- Équations aux dérivées partielles --- Itération (mathématiques) --- 681.3 <063> --- 51 --- 681.3*G1 --- 681.3*G1 Numerical analysis --- Computerwetenschap--Congressen --- Design.