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Numerical Methods for Roots of Polynomials -

Numerical Methods for Roots of Polynomials -
  • Author : J.M. McNamee
  • Publisher :Unknown
  • Release Date :2007-08-17
  • Total pages :354
  • ISBN : 0080489478
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Summary : Numerical Methods for Roots of Polynomials - Part I (along with volume 2 covers most of the traditional methods for polynomial root-finding such as Newton’s, as well as numerous variations on them invented in the last few decades. Perhaps more importantly it covers recent developments such as Vincent’s method, simultaneous iterations, and matrix methods. There is an extensive chapter on evaluation of polynomials, including parallel methods and errors. There are pointers to robust and efficient programs. In short, it could be entitled “A Handbook of Methods for Polynomial Root-finding . This book will be invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic. First comprehensive treatment of Root-Finding in several decades Gives description of high-grade software and where it can be down-loaded Very up-to-date in mid-2006; long chapter on matrix methods Includes Parallel methods, errors where appropriate Invaluable for research or graduate course

Numerical Methods for Roots of Polynomials -

Numerical Methods for Roots of Polynomials -
  • Author : J.M. McNamee,Victor Pan
  • Publisher :Unknown
  • Release Date :2013-07-19
  • Total pages :728
  • ISBN : 9780080931432
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Summary : Numerical Methods for Roots of Polynomials - Part II along with Part I (9780444527295) covers most of the traditional methods for polynomial root-finding such as interpolation and methods due to Graeffe, Laguerre, and Jenkins and Traub. It includes many other methods and topics as well and has a chapter devoted to certain modern virtually optimal methods. Additionally, there are pointers to robust and efficient programs. This book is invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic. First comprehensive treatment of Root-Finding in several decades with a description of high-grade software and where it can be downloaded Offers a long chapter on matrix methods and includes Parallel methods and errors where appropriate Proves invaluable for research or graduate course

Numerical Methods for Roots of Polynomials -

Numerical Methods for Roots of Polynomials -
  • Author : J. M. McNamee,Victor Pan
  • Publisher :Unknown
  • Release Date :2017-11-13
  • Total pages :728
  • ISBN : 0444638350
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Summary : Numerical Methods for Roots of Polynomials - Part II along with Part I (9780444527295) covers most of the traditional methods for polynomial root-finding such as interpolation and methods due to Graeffe, Laguerre, and Jenkins and Traub. It includes many other methods and topics as well and has a chapter devoted to certain modern virtually optimal methods. Additionally, there are pointers to robust and efficient programs. This book is invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic. First comprehensive treatment of Root-Finding in several decades witha description of high-grade software and where it can be downloaded Offers a long chapter on matrix methods and includes Parallel methods and errors where appropriate Proves invaluable for research or graduate course "

Numerical Methods for Roots of Polynomials - Part I

Numerical Methods for Roots of Polynomials - Part I
  • Author : J.M. McNamee,V. Y. Pan
  • Publisher :Unknown
  • Release Date :2007-08-31
  • Total pages :354
  • ISBN : UCSC:32106018795846
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Summary : Numerical Methods for Roots of Polynomials - Part I (along with volume 2 covers most of the traditional methods for polynomial root-finding such as Newton's, as well as numerous variations on them invented in the last few decades. Perhaps more importantly it covers recent developments such as Vincent's method, simultaneous iterations, and matrix methods. There is an extensive chapter on evaluation of polynomials, including parallel methods and errors. There are pointers to robust and efficient programs. In short, it could be entitled "A Handbook of Methods for Polynomial Root-finding”. This book will be invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic. First comprehensive treatment of Root-Finding in several decades Gives description of high-grade software and where it can be down-loaded Very up-to-date in mid-2006; long chapter on matrix methods Includes Parallel methods, errors where appropriate Invaluable for research or graduate course

Handbook of Numerical Methods for the Solution of Algebraic and Transcendental Equations

Handbook of Numerical Methods for the Solution of Algebraic and Transcendental Equations
  • Author : V. L. Zaguskin
  • Publisher :Unknown
  • Release Date :2014-05-12
  • Total pages :216
  • ISBN : 9781483225678
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Summary : Handbook of Numerical Methods for the Solution of Algebraic and Transcendental Equations provides information pertinent to algebraic and transcendental equations. This book indicates a well-grounded plan for the solution of an approximate equation. Organized into six chapters, this book begins with an overview of the solution of various equations. This text then outlines a non-traditional theory of the solution of approximate equations. Other chapters consider the approximate methods for the calculation of roots of algebraic equations. This book discusses as well the methods for making roots more accurate, which are essential in the practical application of Berstoi's method. The final chapter deals with the methods for the solution of simultaneous linear equations, which are divided into direct methods and methods of successive approximation. This book is a valuable resource for students, engineers, and research workers of institutes and industrial enterprises who are using mathematical methods in the solution of technical problems.

Numerical Methods that Work

Numerical Methods that Work
  • Author : Forman S. Acton
  • Publisher :Unknown
  • Release Date :1990
  • Total pages :549
  • ISBN : 0883854503
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Summary : A commonsense approach to numerical algorithms for the solution of equations.

Polynomial Root-finding and Polynomiography

Polynomial Root-finding and Polynomiography
  • Author : Bahman Kalantari
  • Publisher :Unknown
  • Release Date :2009-01
  • Total pages :467
  • ISBN : 9789812700599
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Summary : This book offers fascinating and modern perspectives into the theory and practice of the historical subject of polynomial root-finding, rejuvenating the field via polynomiography, a creative and novel computer visualization that renders spectacular images of a polynomial equation. Polynomiography will not only pave the way for new applications of polynomials in science and mathematics, but also in art and education. The book presents a thorough development of the basic family, arguably the most fundamental family of iteration functions, deriving many surprising and novel theoretical and practical applications such as: algorithms for approximation of roots of polynomials and analytic functions, polynomiography, bounds on zeros of polynomials, formulas for the approximation of Pi, and characterizations or visualizations associated with a homogeneous linear recurrence relation. These discoveries and a set of beautiful images that provide new visions, even of the well-known polynomials and recurrences, are the makeup of a very desirable book. This book is a must for mathematicians, scientists, advanced undergraduates and graduates, but is also for anyone with an appreciation for the connections between a fantastically creative art form and its ancient mathematical foundations.

Numerically Solving Polynomial Systems with Bertini

Numerically Solving Polynomial Systems with Bertini
  • Author : Daniel J. Bates,Jonathan D. Hauenstein,Andrew J. Sommese,Charles W. Wampler
  • Publisher :Unknown
  • Release Date :2013-11-08
  • Total pages :352
  • ISBN : 9781611972696
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Summary : This book is a guide to concepts and practice in numerical algebraic geometry ? the solution of systems of polynomial equations by numerical methods. Through numerous examples, the authors show how to apply the well-received and widely used open-source Bertini software package to compute solutions, including a detailed manual on syntax and usage options. The authors also maintain a complementary web page where readers can find supplementary materials and Bertini input files. Numerically Solving Polynomial Systems with Bertini approaches numerical algebraic geometry from a user's point of view with numerous examples of how Bertini is applicable to polynomial systems. It treats the fundamental task of solving a given polynomial system and describes the latest advances in the field, including algorithms for intersecting and projecting algebraic sets, methods for treating singular sets, the nascent field of real numerical algebraic geometry, and applications to large polynomial systems arising from differential equations. Those who wish to solve polynomial systems can start gently by finding isolated solutions to small systems, advance rapidly to using algorithms for finding positive-dimensional solution sets (curves, surfaces, etc.), and learn how to use parallel computers on large problems. These techniques are of interest to engineers and scientists in fields where polynomial equations arise, including robotics, control theory, economics, physics, numerical PDEs, and computational chemistry.

Inclusion Methods for Nonlinear Problems

Inclusion Methods for Nonlinear Problems
  • Author : Jürgen Herzberger
  • Publisher :Unknown
  • Release Date :2003
  • Total pages :244
  • ISBN : 321183852X
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Summary : The book covers recent developments in the construction and the analysis of numerical algorithms for the solution of nonlinear problems with emphasis on the automatic calculation of guaranteed errorbounds by machine interval operations.The bulk of the presented algorithms deal with problems from various fields in the applied sciences.

Initial Approximations and Root Finding Methods

Initial Approximations and Root Finding Methods
  • Author : Nikolay V. Kyurkchiev
  • Publisher :Unknown
  • Release Date :1998-10-27
  • Total pages :180
  • ISBN : UVA:X004235327
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Summary : Polynomials as mathematical objects have been studied extensively for a long time, and the knowledge collected about them is enormous. Polynomials appear in various fields of applied mathematics and engineering, from mathematics of finance up to signal theory or robust control. The calculation of the roots of a polynomial is a basic problems of numerical mathematics. In this book, an update on iterative methods of calculating simultaneously all roots of a polynomial is given: a survey on basic facts, a lot of methods and properties of those methods connected with the classical task of the approximative determination of roots. For the computer determination the choice of the initial approximation is of special importance. Here the authors offers his new ideas and research results of the last decade which facilitate the practical numerical treatment of polynomials.

Theory Of Difference Equations Numerical Methods And Applications

Theory Of Difference Equations Numerical Methods And Applications
  • Author : V. Lakshmikantham,Donato Trigiante
  • Publisher :Unknown
  • Release Date :2002-06-12
  • Total pages :320
  • ISBN : 9780824744243
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Summary : "Provides a clear and comprehensive overview of the fundamental theories, numerical methods, and iterative processes encountered in difference calculus. Explores classical problems such as orthological polynomials, the Euclidean algorithm, roots of polynomials, and well-conditioning."

Solving Transcendental Equations

Solving Transcendental Equations
  • Author : John P. Boyd
  • Publisher :Unknown
  • Release Date :2014-09-23
  • Total pages :462
  • ISBN : 9781611973525
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Summary : Transcendental equations arise in every branch of science and engineering. While most of these equations are easy to solve, some are not, and that is where this book serves as the mathematical equivalent of a skydiver's reserve parachute--not always needed, but indispensible when it is. The author's goal is to teach the art of finding the root of a single algebraic equation or a pair of such equations.

Advances in Electronic Commerce, Web Application and Communication

Advances in Electronic Commerce, Web Application and Communication
  • Author : David Jin,Sally Lin
  • Publisher :Unknown
  • Release Date :2012-02-24
  • Total pages :622
  • ISBN : 9783642286582
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Summary : ECWAC2012 is an integrated conference devoted to Electronic Commerce, Web Application and Communication. In the this proceedings you can find the carefully reviewed scientific outcome of the second International Conference on Electronic Commerce, Web Application and Communication (ECWAC 2012) held at March 17-18,2012 in Wuhan, China, bringing together researchers from all around the world in the field.

A Concise Introduction to Numerical Analysis

A Concise Introduction to Numerical Analysis
  • Author : A. C. Faul
  • Publisher :Unknown
  • Release Date :2018-10-24
  • Total pages :292
  • ISBN : 9781498712217
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Summary : This textbook provides an accessible and concise introduction to numerical analysis for upper undergraduate and beginning graduate students from various backgrounds. It was developed from the lecture notes of four successful courses on numerical analysis taught within the MPhil of Scientific Computing at the University of Cambridge. The book is easily accessible, even to those with limited knowledge of mathematics. Students will get a concise, but thorough introduction to numerical analysis. In addition the algorithmic principles are emphasized to encourage a deeper understanding of why an algorithm is suitable, and sometimes unsuitable, for a particular problem. A Concise Introduction to Numerical Analysis strikes a balance between being mathematically comprehensive, but not overwhelming with mathematical detail. In some places where further detail was felt to be out of scope of the book, the reader is referred to further reading. The book uses MATLAB® implementations to demonstrate the workings of the method and thus MATLAB's own implementations are avoided, unless they are used as building blocks of an algorithm. In some cases the listings are printed in the book, but all are available online on the book’s page at www.crcpress.com. Most implementations are in the form of functions returning the outcome of the algorithm. Also, examples for the use of the functions are given. Exercises are included in line with the text where appropriate, and each chapter ends with a selection of revision exercises. Solutions to odd-numbered exercises are also provided on the book’s page at www.crcpress.com. This textbook is also an ideal resource for graduate students coming from other subjects who will use numerical techniques extensively in their graduate studies.

Numerical Methods for Engineers and Scientists, Second Edition,

Numerical Methods for Engineers and Scientists, Second Edition,
  • Author : Joe D. Hoffman,Steven Frankel
  • Publisher :Unknown
  • Release Date :2001-05-31
  • Total pages :840
  • ISBN : 0824704436
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Summary : Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative application, and an outline of special features, summing up with a list of tasks students should be able to complete after reading the chapter- perfect for use as a study guide or for review. The AIAA Journal calls the book "...a good, solid instructional text on the basic tools of numerical analysis."

Real Algebraic Geometry

Real Algebraic Geometry
  • Author : Michel Coste,Louis Mahe,Marie-Francoise Roy
  • Publisher :Unknown
  • Release Date :2006-11-15
  • Total pages :420
  • ISBN : 9783540473374
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Summary : Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contributions by: S. Akbulut and H. King; C. Andradas and J. Ruiz; A. Borobia; L. Br|cker; G.W. Brumfield; A. Castilla; Z. Charzynski and P. Skibinski; M. Coste and M. Reguiat; A. Degtyarev; Z. Denkowska; J.-P. Francoise and F. Ronga; J.M. Gamboa and C. Ueno; D. Gondard- Cozette; I.V. Itenberg; P. Jaworski; A. Korchagin; T. Krasinksi and S. Spodzieja; K. Kurdyka; H. Lombardi; M. Marshall and L. Walter; V.F. Mazurovskii; G. Mikhalkin; T. Mostowski and E. Rannou; E.I. Shustin; N. Vorobjov.

Explorations In Numerical Analysis: Python Edition

Explorations In Numerical Analysis: Python Edition
  • Author : James V Lambers,Amber C Sumner Mooney,Vivian Ashley Montiforte
  • Publisher :Unknown
  • Release Date :2021-01-14
  • Total pages :692
  • ISBN : 9789811227950
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Summary : This textbook is intended to introduce advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations.Topics covered include computer arithmetic, error analysis, solution of systems of linear equations, least squares problems, eigenvalue problems, nonlinear equations, optimization, polynomial interpolation and approximation, numerical differentiation and integration, ordinary differential equations, and partial differential equations. For each problem considered, the presentation includes the derivation of solution techniques, analysis of their efficiency, accuracy and robustness, and details of their implementation, illustrated through the Python programming language.This text is suitable for a year-long sequence in numerical analysis, and can also be used for a one-semester course in numerical linear algebra.

Numerical Methods

Numerical Methods
  • Author : Taylor & Francis Group,Wolfgang Boehm
  • Publisher :Unknown
  • Release Date :2020-09-30
  • Total pages :196
  • ISBN : 1138413178
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Summary : This book is written for engineers and other practitioners using numerical methods in their work and serves as a textbook for courses in applied mathematics and numerical analysis.

Calculus

Calculus
  • Author : Gilbert Strang,Edwin "Jed" Herman
  • Publisher :Unknown
  • Release Date :2016-03-30
  • Total pages :229
  • ISBN : 1947172816
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Summary :

Solving Systems of Polynomial Equations

Solving Systems of Polynomial Equations
  • Author : Bernd Sturmfels,Cbms Conference on Solving Polynomial Equations (2002 Texas A & M University)
  • Publisher :Unknown
  • Release Date :2002
  • Total pages :152
  • ISBN : 9780821832516
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Summary : A classic problem in mathematics is solving systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely used across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory, statistics, and numerous other areas. This book furnishes a bridge across mathematical disciplines and exposes many facets of systems of polynomial equations. It covers a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical.The set of solutions to a system of polynomial equations is an algebraic variety - the basic object of algebraic geometry. The algorithmic study of algebraic varieties is the central theme of computational algebraic geometry. Exciting recent developments in computer software for geometric calculations have revolutionized the field. Formerly inaccessible problems are now tractable, providing fertile ground for experimentation and conjecture. The first half of the book gives a snapshot of the state of the art of the topic. Familiar themes are covered in the first five chapters, including polynomials in one variable, Grobner bases of zero-dimensional ideals, Newton polytopes and Bernstein's Theorem, multidimensional resultants, and primary decomposition.The second half of the book explores polynomial equations from a variety of novel and unexpected angles. It introduces interdisciplinary connections, discusses highlights of current research, and outlines possible future algorithms. Topics include computation of Nash equilibria in game theory, semidefinite programming and the real Nullstellensatz, the algebraic geometry of statistical models, the piecewise-linear geometry of valuations and amoebas, and the Ehrenpreis-Palamodov theorem on linear partial differential equations with constant coefficients.Throughout the text, there are many hands-on examples and exercises, including short but complete sessions in MapleR, MATLABR, Macaulay 2, Singular, PHCpack, CoCoA, and SOSTools software. These examples will be particularly useful for readers with no background in algebraic geometry or commutative algebra. Within minutes, readers can learn how to type in polynomial equations and actually see some meaningful results on their computer screens. Prerequisites include basic abstract and computational algebra. The book is designed as a text for a graduate course in computational algebra.

Solving Polynomial Equations

Solving Polynomial Equations
  • Author : Alicia Dickenstein,Ioannis Z. Emiris
  • Publisher :Unknown
  • Release Date :2006-01-27
  • Total pages :426
  • ISBN : 9783540273578
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Summary : The subject of this book is the solution of polynomial equations, that is, s- tems of (generally) non-linear algebraic equations. This study is at the heart of several areas of mathematics and its applications. It has provided the - tivation for advances in di?erent branches of mathematics such as algebra, geometry, topology, and numerical analysis. In recent years, an explosive - velopment of algorithms and software has made it possible to solve many problems which had been intractable up to then and greatly expanded the areas of applications to include robotics, machine vision, signal processing, structural molecular biology, computer-aided design and geometric modelling, as well as certain areas of statistics, optimization and game theory, and b- logical networks. At the same time, symbolic computation has proved to be an invaluable tool for experimentation and conjecture in pure mathematics. As a consequence, the interest in e?ective algebraic geometry and computer algebrahasextendedwellbeyonditsoriginalconstituencyofpureandapplied mathematicians and computer scientists, to encompass many other scientists and engineers. While the core of the subject remains algebraic geometry, it also calls upon many other aspects of mathematics and theoretical computer science, ranging from numerical methods, di?erential equations and number theory to discrete geometry, combinatorics and complexity theory. Thegoalofthisbookistoprovideageneralintroduction tomodernma- ematical aspects in computing with multivariate polynomials and in solving algebraic systems.