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Numerical Methods For For Roots Of Polynomials

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Numerical Methods for Roots of Polynomials

Numerical Methods for Roots of Polynomials   Book
Author : J.M. McNamee
Publisher : Elsevier
Release : 2007-08-17
ISBN : 9780080489476
Language : En, Es, Fr & De

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Book Description :

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   Book
Author : J.M. McNamee,Victor Pan
Publisher : Newnes
Release : 2013-07-19
ISBN : 008093143X
Language : En, Es, Fr & De

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Book Description :

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 Part II

Numerical Methods for Roots of Polynomials   Part II Book
Author : J.M. McNamee,V.Y. Pan
Publisher : Elsevier Inc. Chapters
Release : 2013-07-19
ISBN : 0128077026
Language : En, Es, Fr & De

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Book Description :

We deal here with low-degree polynomials, mostly closed-form solutions. We describe early and modern solutions of the quadratic, and potential errors in these. Again we give the early history of the cubic, and details of Cardan’s solution and Vieta’s trigonometric approach. We consider the discriminant, which decides what type of roots the cubic has. Then we describe several ways (both old and new) of solving the quartic, most of which involve first solving a “resolvent” cubic. The quintic cannot in general be solved by radicals, but can be solved in terms of elliptic or related functions. We describe an algorithm due to Kiepert, which transforms the quintic into a form having no or term; then into a form where the coefficients depend on a single parameter; and later another similar form. This last form can be solved in terms of Weierstrass elliptic and theta functions, and finally the various transformations reversed.

Numerical Methods for Roots of Polynomials Part I

Numerical Methods for Roots of Polynomials   Part I Book
Author : J.M. McNamee,V. Y. Pan
Publisher : Elsevier Science Limited
Release : 2007-08-31
ISBN :
Language : En, Es, Fr & De

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Book Description :

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 Book
Author : J. M. McNamee,Victor Y. Pan
Publisher : Elsevier Science Limited
Release : 2013
ISBN : 9780444527301
Language : En, Es, Fr & De

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Book Description :

This book (along with vol. 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 with a description of high-grade software and where it can be downloadedOffers a long chapter on matrix methods and includes Parallel methods and errors where appropriateProves invaluable for research or graduate course.

Numerical Methods for Engineers and Scientists Second Edition

Numerical Methods for Engineers and Scientists  Second Edition  Book
Author : Joe D. Hoffman,Steven Frankel
Publisher : CRC Press
Release : 2001-05-31
ISBN : 9780824704438
Language : En, Es, Fr & De

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Book Description :

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."

The Numerical Solution of Systems of Polynomials Arising in Engineering and Science

The Numerical Solution of Systems of Polynomials Arising in Engineering and Science Book
Author : Andrew J Sommese,Charles W Wampler II
Publisher : World Scientific
Release : 2005-03-21
ISBN : 9814480886
Language : En, Es, Fr & De

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Book Description :

' Written by the founders of the new and expanding field of numerical algebraic geometry, this is the first book that uses an algebraic-geometric approach to the numerical solution of polynomial systems and also the first one to treat numerical methods for finding positive dimensional solution sets. The text covers the full theory from methods developed for isolated solutions in the 1980's to the most recent research on positive dimensional sets. Contents:Background:Polynomial SystemsHomotopy ContinuationProjective SpacesGenericity and Probability OnePolynomials of One VariableOther MethodsIsolated Solutions:Coefficient-Parameter HomotopyPolynomial StructuresCase StudiesEndpoint EstimationChecking Results and Other Implementation TipsPositive Dimensional Solutions:Basic Algebraic GeometryBasic Numerical Algebraic GeometryA Cascade Algorithm for Witness SupersetsThe Numerical Irreducible DecompositionThe Intersection of Algebraic SetsAppendices:Algebraic GeometrySoftware for Polynomial ContinuationHomLab User's Guide Readership: Graduate students and researchers in applied mathematics and mechanical engineering. Keywords:Polynomial Systems;Numerical Methods;Homotopy Methods;Mechanical Engineering;Numerical Algebraic Geometry;Kinematics;RoboticsKey Features:Useful introduction to the field for graduate students and researchers in related areasIncludes exercises suitable for classroom use and self-studyIncludes Matlab software to illustrate the methodIncludes many graphical illustrationsIncludes a detailed summary of useful results from algebraic geometryReviews:“The text is written in a very smooth and intelligent form, yielding a readable book whose contents are accessible to a wide class of readers, even to undergraduate students, provided that they accept that some delicate points of some of the proofs could be omitted. Its readability and fast access to the core of the book makes it recommendable as a pleasant read.”Mathematical Reviews “This is an excellent book on numerical solutions of polynomials systems for engineers, scientists and numerical analysts. As pioneers of the field of numerical algebraic geometry, the authors have provided a comprehensive summary of ideas, methods, problems of numerical algebraic geometry and applications to solving polynomial systems. Through the book readers will experience the authors' original ideas, contributions and their techniques in handling practical problems … Many interesting examples from engineering and science have been used throughout the book. Also the exercises are well designed in line with the content, along with the algorithms, sample programs in Matlab and author's own software 'HOMLAB' for polynomial continuation. This is a remarkable book that I recommend to engineers, scientists, researchers, professionals and students, and particularly numerical analysts who will benefit from the rapid development of numerical algebraic geometry.”Zentralblatt MATH '

Initial Approximations and Root Finding Methods

Initial Approximations and Root Finding Methods Book
Author : Nikolay V. Kyurkchiev
Publisher : Wiley-VCH
Release : 1998-10-27
ISBN :
Language : En, Es, Fr & De

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Book Description :

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.

Numerical Methods for Scientists and Engineers

Numerical Methods for Scientists and Engineers Book
Author : H.M. Antia
Publisher : Springer Science & Business Media
Release : 2002-05-01
ISBN : 9783764367152
Language : En, Es, Fr & De

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Book Description :

This book presents an exhaustive and in-depth exposition of the various numerical methods used in scientific and engineering computations. It emphasises the practical aspects of numerical computation and discusses various techniques in sufficient detail to enable their implementation in solving a wide range of problems.

Numerical Methods for Engineers

Numerical Methods for Engineers Book
Author : Santosh K Gupta
Publisher : New Age International
Release : 1995
ISBN : 9788122406511
Language : En, Es, Fr & De

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Book Description :

This Book Is Intended To Be A Text For Either A First Or A Second Course In Numerical Methods For Students In All Engineering Disciplines. Difficult Concepts, Which Usually Pose Problems To Students Are Explained In Detail And Illustrated With Solved Examples. Enough Elementary Material That Could Be Covered In The First-Level Course Is Included, For Example, Methods For Solving Linear And Nonlinear Algebraic Equations, Interpolation, Differentiation, Integration, And Simple Techniques For Integrating Odes And Pdes (Ordinary And Partial Differential Equations).Advanced Techniques And Concepts That Could Form Part Of A Second-Level Course Includegears Method For Solving Ode-Ivps (Initial Value Problems), Stiffness Of Ode- Ivps, Multiplicity Of Solutions, Convergence Characteristics, The Orthogonal Collocation Method For Solving Ode-Bvps (Boundary Value Problems) And Finite Element Techniques. An Extensive Set Of Graded Problems, Often With Hints, Has Been Included.Some Involve Simple Applications Of The Concepts And Can Be Solved Using A Calculator, While Several Are From Real-Life Situations And Require Writing Computer Programs Or Use Of Library Subroutines. Practice On These Is Expected To Build Up The Reader'S Confidence In Developing Large Computer Codes.

Numerical Methods for Nonlinear Engineering Models

Numerical Methods for Nonlinear Engineering Models Book
Author : John R. Hauser
Publisher : Springer Science & Business Media
Release : 2009-03-24
ISBN : 1402099207
Language : En, Es, Fr & De

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Book Description :

There are many books on the use of numerical methods for solving engineering problems and for modeling of engineering artifacts. In addition there are many styles of such presentations ranging from books with a major emphasis on theory to books with an emphasis on applications. The purpose of this book is hopefully to present a somewhat different approach to the use of numerical methods for - gineering applications. Engineering models are in general nonlinear models where the response of some appropriate engineering variable depends in a nonlinear manner on the - plication of some independent parameter. It is certainly true that for many types of engineering models it is sufficient to approximate the real physical world by some linear model. However, when engineering environments are pushed to - treme conditions, nonlinear effects are always encountered. It is also such - treme conditions that are of major importance in determining the reliability or failure limits of engineering systems. Hence it is essential than engineers have a toolbox of modeling techniques that can be used to model nonlinear engineering systems. Such a set of basic numerical methods is the topic of this book. For each subject area treated, nonlinear models are incorporated into the discussion from the very beginning and linear models are simply treated as special cases of more general nonlinear models. This is a basic and fundamental difference in this book from most books on numerical methods.

An Introduction to Numerical Methods in C

An Introduction to Numerical Methods in C   Book
Author : Brian Hilton Flowers,Sir Brian Hilton Flowers,Fellow and Former Rector B H Flowers
Publisher : Oxford University Press on Demand
Release : 2000
ISBN : 9780198506935
Language : En, Es, Fr & De

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Book Description :

This text on numerical computing, presented through the medium of the C++ language, is designed for students of science and engineering who are serriously studying nummerical methods for the first time. It should also be of interest to computing scientists who wish to see how C++ can be used in earnest for nummerical computation. The mathematical prerequisites are those which an undergraduate student of science or engineering might be expected to possess after the earlier years of study: elementary calculus, linear algebra, and differential equations. In computing, a good knowledge, such as Basic, Fortran, or Pascal, is asumed, while a working knowledge of C would be an advantage. However, no prior knowledge of C++ is assumed. The language is developed in step with its numerical applications. Features of the language not used here are ignored. What remains, however, is a powerful framework for numerical computations and more than enough for an introductory text.

Numerical Methods that Work

Numerical Methods that Work Book
Author : Forman S. Acton
Publisher : MAA
Release : 1990
ISBN : 9780883854501
Language : En, Es, Fr & De

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Book Description :

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

Principles of Numerical Analysis

Principles of Numerical Analysis Book
Author : Alston S. Householder
Publisher : Courier Corporation
Release : 2006-09
ISBN : 048645312X
Language : En, Es, Fr & De

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Book Description :

Computer science rests upon the building blocks of numerical analysis. This concise treatment by an expert covers the essentials of the solution of finite systems of linear and nonlinear equations as well as the approximate representation of functions. A final section provides 54 problems, subdivided according to chapter. 1953 edition.

Numerical Methods

Numerical Methods Book
Author : M. K. Jain,Satteluri R. K. Iyengar,Rajinder Kumar Jain
Publisher : New Age International
Release : 2007-01-01
ISBN : 8122415342
Language : En, Es, Fr & De

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Book Description :

Is An Outline Series Containing Brief Text Of Numerical Solution Of Transcendental And Polynomial Equations, System Of Linear Algebraic Equations And Eigenvalue Problems, Interpolation And Approximation, Differentiation And Integration, Ordinary Differential Equations And Complete Solutions To About 300 Problems. Most Of These Problems Are Given As Unsolved Problems In The Authors Earlier Book. User Friendly Turbo Pascal Programs For Commonly Used Numerical Methods Are Given In The Appendix. This Book Can Be Used As A Text/Help Book Both By Teachers And Students.

Numerical Analysis Using MATLAB and Spreadsheets

Numerical Analysis Using MATLAB and Spreadsheets Book
Author : Steven T. Karris
Publisher : Orchard Publications
Release : 2004
ISBN : 0974423912
Language : En, Es, Fr & De

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Book Description :

Annotation This text provides complete, clear, and detailed explanations of the principal numerical analysis methods and well known functions used in science and engineering. These are illustrated with many practical examples. With this text the reader learns numerical analysis with many real-world applications, MATLAB, and spreadsheets simultaneously. This text includes the following chapters:? Introduction to MATLAB? Root Approximations? Sinusoids and Complex Numbers? Matrices and Determinants? Review of Differential Equations? Fourier, Taylor, and Maclaurin Series? Finite Differences and Interpolation? Linear and Parabolic Regression? Solution of Differential Equations by Numerical Methods? Integration by Numerical Methods? Difference Equations? Partial Fraction Expansion? The Gamma and Beta Functions? Orthogonal Functions and Matrix Factorizations? Bessel, Legendre, and Chebyshev Polynomials? Optimization MethodsEach chapter contains numerous practical applications supplemented with detailed instructionsfor using MATLAB and/or Microsoft Excel? to obtain quick solutions.

Numerical Analysis for Engineers and Scientists

Numerical Analysis for Engineers and Scientists Book
Author : G. Miller
Publisher : Cambridge University Press
Release : 2014-05-29
ISBN : 1107021081
Language : En, Es, Fr & De

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Book Description :

Graduate-level introduction balancing theory and application. Provides full coverage of classical methods with many practical examples and demonstration programs.

An Introduction to Numerical Methods and Analysis

An Introduction to Numerical Methods and Analysis Book
Author : James F. Epperson
Publisher : John Wiley & Sons
Release : 2013-10-07
ISBN : 1118367596
Language : En, Es, Fr & De

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Book Description :

Praise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises."—Zentralblatt MATH ". . . carefully structured with many detailed worked examples."—The Mathematical Gazette The Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis. An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and Clenshaw-Curtis quadrature, are presented from an introductory perspective, and the Second Edition also features: Chapters and sections that begin with basic, elementary material followed by gradual coverage of more advanced material Exercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercises Widespread exposure and utilization of MATLAB An appendix that contains proofs of various theorems and other material The book is an ideal textbook for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.

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

Handbook of Numerical Methods for the Solution of Algebraic and Transcendental Equations Book
Author : V. L. Zaguskin
Publisher : Elsevier
Release : 2014-05-12
ISBN : 1483225674
Language : En, Es, Fr & De

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Book Description :

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.