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Over and over again
Authors: --- --- ---
ISBN: 088385953X 9780883859537 0883856417 9780883856413 Year: 1997 Publisher: Washington, DC : Mathematical Association of America,

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Suitable as supplemental reading in courses in differential and integral calculus, numerical analysis, approximation theory and computer-aided 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, BŽzier 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 computer-aided geometric design.


Book
Operators and iterative processes of fejér type : theory and applications
Authors: --- ---
ISBN: 1282187953 9786612187957 3110218194 9783110218190 3110218186 9783110218183 9781282187955 9783110218183 Year: 2009 Publisher: Berlin ; New York : W. de Gruyter,

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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, self-contained 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.


Book
Iterative algorithms.
Authors: --- --- --- ---
ISBN: 1634854225 9781634854061 1634854063 9781634858793 1634858794 9781634854221 Year: 2017 Publisher: New York : Nova Publishers,

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Iterative algorithms
Authors: --- --- --- --- --- et al.
ISBN: 1634858964 9781634858960 9781634858793 Year: 2017 Publisher: New York : Nova Publishers,

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Solving polynomial equation systems II : Macaulay's paradigm and Gröbner technology
Authors: ---
ISBN: 9781107340954 9780521811569 1107340950 9781107266902 1107266904 9781299707610 1299707610 9781107269989 1107269989 9780521811545 0521811546 0521811562 9780521811552 0521811554 1139883003 1107266556 110726443X 1107263344 1107267978 Year: 2005 Volume: v. 99 Publisher: Cambridge ; New York : Cambridge University Press,

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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.

Solving polynomial equation systems
Authors: ---
ISBN: 9780511542831 9780521811545 0511064497 9780511064494 0511542836 0511072953 9780511072956 1280418559 9786610418558 0511178883 1139147919 0511058160 0511306024 Year: 2003 Publisher: Cambridge ; New York : Cambridge University Press,

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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.

Computational theory of iterative methods
Authors: --- --- ---
ISBN: 1281189189 9786611189181 0080560709 0444531629 9780444531629 9780080560700 9781281189189 6611189181 Year: 2007 Volume: 15 Publisher: Amsterdam ; London : Elsevier,

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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


Book
Some successive approximation methods in control and oscillation theory
Authors: --- --- --- --- --- et al.
ISBN: 1283525372 9786613837820 0080955681 9780080955681 9780122479502 0122479505 Year: 1969 Publisher: New York : Academic Press,

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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 non-Lagrange 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 low-rank


Book
Iterative methods in combinatorial optimization
Authors: --- --- ---
ISBN: 9780521189439 9781107007512 0521189438 1107007518 9780511977152 9781139081078 1139081071 9781139078801 1139078801 0511977158 9781283111164 1283111160 1107221773 9786613111166 1139076523 1139083341 1139070800 Year: 2011 Publisher: Cambridge ; New York : Cambridge University Press,

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"With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual 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 NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual 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"--

Geometric methods for discrete dynamical systems
Author:
ISBN: 1280442123 9786610442126 1423735234 0195359046 1601299494 9781423735236 9781601299499 9780195085457 0195085450 0195085450 Year: 1998 Publisher: New York ; Oxford, [England] : Oxford University Press,

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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 round-off 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 chain-recurrence play a central role in the treatment. The book wi

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