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Suitable as supplemental reading in courses in differential and integral calculus, numerical analysis, approximation theory and computeraided geometric design. Relations of mathematical objects to each other are expressed by transformations. The repeated application of a transformation over and over again, i.e., its iteration leads to solution of equations, as in Newton's method for finding roots, or Picard's method for solving differential equations. This book studies a treasure trove of iterations, in number theory, analysis and geometry, and applied them to various problems, many of them taken from international and national Mathematical Olympiad competitions. Among topics treated are classical and not so classical inequalities, Sharkovskii's theorem, interpolation, Bernstein polynomials, Bzier curves and surfaces, and splines. Most of the book requires only high school mathematics; the last part requires elementary calculus. This book would be an excellent supplement to courses in calculus, differential equations,, numerical analysis, approximation theory and computeraided geometric design.
Iterative methods (Mathematics)  Transformations (Mathematics)  Algorithms  Differential invariants  Geometry, Differential  Iteration (Mathematics)  Numerical analysis
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This book, written by two experts in the field, deals with classes of iterative methods for the approximate solution of fixed points equations for operators satisfying a special contractivity condition, the Fejér property. The book is elementary, selfcontained and uses methods from functional analysis, with a special focus on the construction of iterative schemes. Applications to parallelization, randomization and linear programming are also considered.
Iterative methods (Mathematics)  Numerical analysis.  Mathematical analysis  Iteration (Mathematics)  Numerical analysis
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Iterative methods (Mathematics)  Algorithms.  Numerical analysis.  Mathematical analysis  Algorism  Algebra  Arithmetic  Iteration (Mathematics)  Numerical analysis  Foundations
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Iterative methods (Mathematics)  Algorithms.  Numerical analysis.  Mathematical analysis  Algorism  Algebra  Arithmetic  Iteration (Mathematics)  Numerical analysis  Foundations
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The second volume of a comprehensive treatise. This part focuses on Buchberger theory and its application to the algorithmic view of commutative algebra.
Equations  Polynomials.  Iterative methods (Mathematics)  Iteration (Mathematics)  Numerical analysis  Algebra  Algebra  Numerical solutions.  Graphic methods
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Mora covers the classical theory of finding roots of a univariate polynomial, emphasising computational aspects. He shows that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate polynomials.
Equations  Polynomials.  Iterative methods (Mathematics)  Iteration (Mathematics)  Numerical analysis  Algebra  Numerical solutions.  Graphic methods
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The book is designed for researchers, students and practitioners interested in using fast and efficient iterative methods to approximate solutions of nonlinear equations. The following four major problems are addressed. Problem 1: Show that the iterates are well defined. Problem 2: concerns the convergence of the sequences generated by a process and the question of whether the limit points are, in fact solutions of the equation. Problem 3: concerns the economy of the entire operations. Problem 4: concerns with how to best choose a method, algorithm or software program to solve a specific type
Funktionalanalysis.  Iteration.  Iterative methods (Mathematics).  Lehrbuch.  Numerische Mathematik.  Iterative methods (Mathematics)  Engineering & Applied Sciences  Applied Mathematics  Numerical analysis.  Mathematical analysis  Iteration (Mathematics)  Numerical analysis
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In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a nonLagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for lowrank
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"With the advent of approximation algorithms for NPhard combinatorial optimization problems, several techniques from exact optimization such as the primaldual method have proven their staying power and versatility. This book describes a simple and powerful method that is iterative in essence, and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids, and flows. The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Discussions of advanced applications illustrate their potential for future application in research in approximation algorithms" "With the advent of approximation algorithms for NPhard combinatorial optimization problems, several techniques from exact optimization such as the primaldual method have proven their staying power and versatility. This book describes a simple and powerful method that is iterative in essence and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids, and flows. The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Discussions of advanced applications illustrate their potential for future application in research in approximation algorithms"
Iterative methods (Mathematics)  Combinatorial optimization  Itération (Mathématiques)  Optimisation combinatoire  Combinatorial optimization.  Optimization, Combinatorial  Combinatorial analysis  Mathematical optimization  Iteration (Mathematics)  Numerical analysis
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This book looks at dynamics as an iteration process where the output of a function is fed back as an input to determine the evolution of an initial state over time. The theory examines errors which arise from roundoff in numerical simulations, from the inexactness of mathematical models used to describe physical processes, and from the effects of external controls. The author provides an introduction accessible to beginning graduate students and emphasizing geometric aspects of the theory. Conley's ideas about rough orbits and chainrecurrence play a central role in the treatment. The book wi
Differentiable dynamical systems.  Iterative methods (Mathematics)  Iteration (Mathematics)  Numerical analysis  Differential dynamical systems  Dynamical systems, Differentiable  Dynamics, Differentiable  Differential equations  Global analysis (Mathematics)  Topological dynamics
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