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Iterative methods (Mathematics)  Numerical analysis.  Mathematical analysis  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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Polynomial equations have been long studied, both theoretically and with a view to solving them. Until recently, manual computation was the only solution method and the theory was developed to accommodate it. With the advent of computers, the situation changed dramatically. Many classical results can be more usefully recast within a different framework which in turn lends itself to further theoretical development tuned to computation. This first book in a trilogy is devoted to the new approach. It is a handbook covering the classical theory of finding roots of a univariate polynomial, emphasising computational aspects, especially the representation and manipulation of algebraic numbers, enlarged by more recent representations like the Duval Model and the Thom Codification. Mora aims to show 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  Polynomials
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Iterative methods (Mathematics)  Numerical analysis.  Mathematical analysis  Iteration (Mathematics)  Numerical analysis
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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.
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Differential operators  Iterative methods (Mathematics)  517  517 Analysis  Analysis  Iteration (Mathematics)  Numerical analysis  Operators, Differential  Differential equations  Operator theory
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Iterative methods (Mathematics)  Mappings (Mathematics)  Maps (Mathematics)  Functions  Functions, Continuous  Topology  Transformations (Mathematics)  Iteration (Mathematics)  Numerical analysis
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Operator equations  Nonlinear operators.  Iterative methods (Mathematics)  Iteration (Mathematics)  Numerical analysis  Operators, Nonlinear  Operator theory  Numerical solutions.
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