Numerical Methods for Roots of Polynomials

Numerical Methods for Roots of Polynomials
Author: J.M. McNamee
Publsiher: Elsevier
Total Pages: 354
Release: 2007-08-17
ISBN 10: 9780080489476
ISBN 13: 0080489478
Language: EN, FR, DE, ES & NL

Numerical Methods for Roots of Polynomials Book Review:

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
Publsiher: Newnes
Total Pages: 728
Release: 2013-07-19
ISBN 10: 008093143X
ISBN 13: 9780080931432
Language: EN, FR, DE, ES & NL

Numerical Methods for Roots of Polynomials Book Review:

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
Publsiher: Studies in Computational Mathe
Total Pages: 728
Release: 2017-11-13
ISBN 10: 9780444638359
ISBN 13: 0444638350
Language: EN, FR, DE, ES & NL

Numerical Methods for Roots of Polynomials Book Review:

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
Publsiher: Elsevier Science Limited
Total Pages: 354
Release: 2007-08-31
ISBN 10:
ISBN 13: UCSC:32106018795846
Language: EN, FR, DE, ES & NL

Numerical Methods for Roots of Polynomials Part I Book Review:

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
Publsiher: Elsevier
Total Pages: 216
Release: 2014-05-12
ISBN 10: 1483225674
ISBN 13: 9781483225678
Language: EN, FR, DE, ES & NL

Handbook of Numerical Methods for the Solution of Algebraic and Transcendental Equations Book Review:

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
Publsiher: MAA
Total Pages: 549
Release: 1990
ISBN 10: 9780883854501
ISBN 13: 0883854503
Language: EN, FR, DE, ES & NL

Numerical Methods that Work Book Review:

A commonsense approach to numerical algorithms for the solution of equations.

Polynomial Root finding and Polynomiography

Polynomial Root finding and Polynomiography
Author: Bahman Kalantari
Publsiher: World Scientific
Total Pages: 467
Release: 2009-01
ISBN 10: 9812700595
ISBN 13: 9789812700599
Language: EN, FR, DE, ES & NL

Polynomial Root finding and Polynomiography Book Review:

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
Publsiher: SIAM
Total Pages: 352
Release: 2013-11-08
ISBN 10: 1611972698
ISBN 13: 9781611972696
Language: EN, FR, DE, ES & NL

Numerically Solving Polynomial Systems with Bertini Book Review:

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
Publsiher: Springer Science & Business Media
Total Pages: 244
Release: 2003
ISBN 10: 9783211838525
ISBN 13: 321183852X
Language: EN, FR, DE, ES & NL

Inclusion Methods for Nonlinear Problems Book Review:

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
Publsiher: Wiley-VCH
Total Pages: 180
Release: 1998-10-27
ISBN 10:
ISBN 13: UVA:X004235327
Language: EN, FR, DE, ES & NL

Initial Approximations and Root Finding Methods Book Review:

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
Publsiher: CRC Press
Total Pages: 320
Release: 2002-06-12
ISBN 10: 0824744241
ISBN 13: 9780824744243
Language: EN, FR, DE, ES & NL

Theory Of Difference Equations Numerical Methods And Applications Book Review:

"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."

Advances in Electronic Commerce Web Application and Communication

Advances in Electronic Commerce  Web Application and Communication
Author: David Jin,Sally Lin
Publsiher: Springer Science & Business Media
Total Pages: 622
Release: 2012-02-24
ISBN 10: 3642286585
ISBN 13: 9783642286582
Language: EN, FR, DE, ES & NL

Advances in Electronic Commerce Web Application and Communication Book Review:

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.

Solving Transcendental Equations

Solving Transcendental Equations
Author: John P. Boyd
Publsiher: SIAM
Total Pages: 462
Release: 2014-09-23
ISBN 10: 161197352X
ISBN 13: 9781611973525
Language: EN, FR, DE, ES & NL

Solving Transcendental Equations Book Review:

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.

Numerical Methods

Numerical Methods
Author: Taylor & Francis Group,Wolfgang Boehm
Publsiher: A K PETERS
Total Pages: 196
Release: 2020-09-30
ISBN 10: 9781138413177
ISBN 13: 1138413178
Language: EN, FR, DE, ES & NL

Numerical Methods Book Review:

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.

Numerical Methods for Engineers and Scientists Second Edition

Numerical Methods for Engineers and Scientists  Second Edition
Author: Joe D. Hoffman,Steven Frankel
Publsiher: CRC Press
Total Pages: 840
Release: 2001-05-31
ISBN 10: 9780824704438
ISBN 13: 0824704436
Language: EN, FR, DE, ES & NL

Numerical Methods for Engineers and Scientists Second Edition Book Review:

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."

An Introduction to Numerical Methods and Analysis

An Introduction to Numerical Methods and Analysis
Author: James F. Epperson
Publsiher: John Wiley & Sons
Total Pages: 663
Release: 2013-06-06
ISBN 10: 1118626230
ISBN 13: 9781118626238
Language: EN, FR, DE, ES & NL

An Introduction to Numerical Methods and Analysis Book Review:

Praise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises." —Zentrablatt Math ". . . carefully structured with many detailed worked examples . . ." —The Mathematical Gazette ". . . an up-to-date and user-friendly account . . ." —Mathematika An Introduction to Numerical Methods and Analysis addresses the mathematics underlying approximation and scientific computing and successfully explains where approximation methods come from, why they sometimes work (or don't work), and when to use one of the many techniques that are available. Written in a style that emphasizes readability and usefulness for the numerical methods novice, the book begins with basic, elementary material and gradually builds up to more advanced topics. A selection of concepts required for the study of computational mathematics is introduced, and simple approximations using Taylor's Theorem are also treated in some depth. The text includes exercises that run the gamut from simple hand computations, to challenging derivations and minor proofs, to programming exercises. A greater emphasis on applied exercises as well as the cause and effect associated with numerical mathematics is featured throughout the book. An Introduction to Numerical Methods and Analysis is the ideal text for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.

Real Algebraic Geometry

Real Algebraic Geometry
Author: Michel Coste,Louis Mahe,Marie-Francoise Roy
Publsiher: Springer
Total Pages: 420
Release: 2006-11-15
ISBN 10: 3540473378
ISBN 13: 9783540473374
Language: EN, FR, DE, ES & NL

Real Algebraic Geometry Book Review:

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
Publsiher: World Scientific
Total Pages: 692
Release: 2021-01-14
ISBN 10: 9811227950
ISBN 13: 9789811227950
Language: EN, FR, DE, ES & NL

Explorations In Numerical Analysis Python Edition Book Review:

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.

Solving Systems of Polynomial Equations

Solving Systems of Polynomial Equations
Author: Bernd Sturmfels,Cbms Conference on Solving Polynomial Equations (2002 Texas A & M University)
Publsiher: American Mathematical Soc.
Total Pages: 152
Release: 2002
ISBN 10: 0821832514
ISBN 13: 9780821832516
Language: EN, FR, DE, ES & NL

Solving Systems of Polynomial Equations Book Review:

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.

Calculus

Calculus
Author: Gilbert Strang,Edwin "Jed" Herman
Publsiher: Unknown
Total Pages: 329
Release: 2016-03-30
ISBN 10: 9781947172814
ISBN 13: 1947172816
Language: EN, FR, DE, ES & NL

Calculus Book Review: