Numerical Methods for Roots of Polynomials   Book

Numerical Methods for Roots of Polynomials


  • Author : J.M. McNamee
  • Publisher : Elsevier
  • Release Date : 2007-08-17
  • Genre: Mathematics
  • Pages : 354
  • ISBN 10 : 0080489478

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Numerical Methods for Roots of Polynomials Excerpt :

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   Book

Numerical Methods for Roots of Polynomials


  • Author : J.M. McNamee
  • Publisher : Newnes
  • Release Date : 2013-07-19
  • Genre: Mathematics
  • Pages : 728
  • ISBN 10 : 9780080931432

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Numerical Methods for Roots of Polynomials Excerpt :

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 Engineers and Scientists Book
Score: 5
From 1 Ratings

Numerical Methods for Engineers and Scientists


  • Author : Joe D. Hoffman
  • Publisher : CRC Press
  • Release Date : 2018-10-03
  • Genre: Mathematics
  • Pages : 840
  • ISBN 10 : 9781482270600

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Numerical Methods for Engineers and Scientists Excerpt :

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."

Numerical Methods for Roots of Polynomials   Part II Book

Numerical Methods for Roots of Polynomials Part II


  • Author : J.M. McNamee
  • Publisher : Elsevier Inc. Chapters
  • Release Date : 2013-07-19
  • Genre: Mathematics
  • Pages : 728
  • ISBN 10 : 9780128076989

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Numerical Methods for Roots of Polynomials Part II Excerpt :

We discuss Graeffes’s method and variations. Graeffe iteratively computes a sequence of polynomialsso that the roots of are those of raised to the power . Then the roots of can be expressed in terms of the coefficients of . Special treatment is given to complex and/or multiple modulus roots. A method of Lehmer’s finds the argument as well as the modulus of the roots, while other authors show how to reduce the danger of overflow. Variants such as the Chebyshev-like process are discussed. The Graeffe iteration lends itself well to parallel processing, and two algorithms in that context are described. Error estimates are given, as well as several variants.

Introduction to Numerical Analysis Using MATLAB   Book
Score: 5
From 2 Ratings

Introduction to Numerical Analysis Using MATLAB


  • Author : Butt
  • Publisher : Jones & Bartlett Learning
  • Release Date : 2009-02-17
  • Genre: Mathematics
  • Pages : 600
  • ISBN 10 : 076377376X

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Introduction to Numerical Analysis Using MATLAB Excerpt :

Numerical analysis is the branch of mathematics concerned with the theoretical foundations of numerical algorithms for the solution of problems arising in scientific applications. Designed for both courses in numerical analysis and as a reference for practicing engineers and scientists, this book presents the theoretical concepts of numerical analysis and the practical justification of these methods are presented through computer examples with the latest version of MATLAB. The book addresses a variety of questions ranging from the approximation of functions and integrals to the approximate solution of algebraic, transcendental, differential and integral equations, with particular emphasis on the stability, accuracy, efficiency and reliability of numerical algorithms. The CD-ROM which accompanies the book includes source code, a numerical toolbox, executables, and simulations.

Exploring Numerical Methods Book

Exploring Numerical Methods


  • Author : Peter Linz
  • Publisher : Jones & Bartlett Learning
  • Release Date : 2003
  • Genre: Computers
  • Pages : 473
  • ISBN 10 : 0763714992

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Exploring Numerical Methods Excerpt :

Advanced Mathematics

Fundamental Numerical Methods for Electrical Engineering Book

Fundamental Numerical Methods for Electrical Engineering


  • Author : Stanislaw Rosloniec
  • Publisher : Springer Science & Business Media
  • Release Date : 2008-07-17
  • Genre: Technology & Engineering
  • Pages : 284
  • ISBN 10 : 9783540795193

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Fundamental Numerical Methods for Electrical Engineering Excerpt :

Stormy development of electronic computation techniques (computer systems and software), observed during the last decades, has made possible automation of data processing in many important human activity areas, such as science, technology, economics and labor organization. In a broadly understood technology area, this developmentledtoseparationofspecializedformsofusingcomputersforthedesign and manufacturing processes, that is: – computer-aided design (CAD) – computer-aided manufacture (CAM) In order to show the role of computer in the rst of the two applications m- tioned above, let us consider basic stages of the design process for a standard piece of electronic system, or equipment: – formulation of requirements concerning user properties (characteristics, para- ters) of the designed equipment, – elaboration of the initial, possibly general electric structure, – determination of mathematical model of the system on the basis of the adopted electric structure, – determination of basic responses (frequency- or time-domain) of the system, on the base of previously established mathematical model, – repeated modi cation of the adopted diagram (changing its structure or element values) in case, when it does not satisfy the adopted requirements, – preparation of design and technological documentation, – manufacturing of model (prototype) series, according to the prepared docum- tation, – testing the prototype under the aspect of its electric properties, mechanical du- bility and sensitivity to environment conditions, – modi cation of prototype documentation, if necessary, and handing over the documentation to series production. The most important stages of the process under discussion are illustrated in Fig. I. 1. xi xii Introduction Fig. I.

Object Oriented Implementation of Numerical Methods Book

Object Oriented Implementation of Numerical Methods


  • Author : Didier H. Besset
  • Publisher : Morgan Kaufmann
  • Release Date : 2001
  • Genre: Computers
  • Pages : 766
  • ISBN 10 : 1558606793

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Object Oriented Implementation of Numerical Methods Excerpt :

"There are few books that show how to build programs of any kind. One common theme is compiler building, and there are shelves full of them. There are few others. It's an area, or a void, that needs filling. this book does a great job of showing how to build numerical analysis programs." -David N. Smith, IBM T J Watson Research Center Numerical methods naturally lend themselves to an object-oriented approach. Mathematics builds high- level ideas on top of previously described, simpler ones. Once a property is demonstrated for a given concept, it can be applied to any new concept sharing the same premise as the original one, similar to the ideas of reuse and inheritance in object-oriented (OO) methodology. Few books on numerical methods teach developers much about designing and building good code. Good computing routines are problem-specific. Insight and understanding are what is needed, rather than just recipes and black box routines. Developers need the ability to construct new programs for different applications. Object-Oriented Implementation of Numerical Methods reveals a complete OO design methodology in a clear and systematic way. Each method is presented in a consistent format, beginning with a short explanation and following with a description of the general OO architecture for the algorithm. Next, the code implementations are discussed and presented along with real-world examples that the author, an experienced software engineer, has used in a variety of commercial applications. Features: Reveals the design methodology behind the code, including design patterns where appropriate, rather than just presenting canned solutions. Implements all methods side by side in both Java and Smalltalk. This contrast can significantly enhance your understanding of the nature of OO programming languages. Provides a step-by-step pathway to new object-oriented techniques for programmers familiar with using procedural languages such as C or Fortran for numerical methods. Inclu

Numerical Methods for Roots of Polynomials   Part II Book

Numerical Methods for Roots of Polynomials Part II


  • Author : J.M. McNamee
  • Publisher : Elsevier Inc. Chapters
  • Release Date : 2013-07-19
  • Genre: Mathematics
  • Pages : 728
  • ISBN 10 : 9780128077054

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Numerical Methods for Roots of Polynomials Part II Excerpt :

The zeros of a polynomial can be readily recovered from its linear factors. The linear factors can be approximated by first splitting a polynomial numerically into the product of its two nonconstant factors and then recursively splitting every computed nonlinear factor in similar fashion. For both the worst and average case inputs the resulting algorithms solve the polynomial factorization and root-finding problems within fixed sufficiently small error bounds by using nearly optimal arithmetic and Boolean time, that is using nearly optimal numbers of arithmetic and bitwise operations; in the case of a polynomial with integer coefficients and simple roots we can immediately extend factorization to root isolation, that is to computing disjoint covering discs, one for every root on the complex plane. The presented algorithms compute highly accurate approximations to all roots nearly as fast as one reads the input coefficients. Furthermore, our algorithms allow processor efficient parallel acceleration, which enables root-finding, factorization, and root isolation in polylogarithmic arithmetic and Boolean time. The chapter thoroughly covers the design and analysis of these algorithms, including auxiliary techniques of independent interest. At the end we compare the presented polynomial root-finders with alternative ones, in particular with the popular algorithms adopted by users based on supporting empirical information. We also comment on some promising directions to further progress.

Numerical Methods for Roots of Polynomials Book

Numerical Methods for Roots of Polynomials


  • Author : J. M. McNamee
  • Publisher : Unknown
  • Release Date : 2007
  • Genre: Equations, Roots of
  • Pages : 364
  • ISBN 10 : UCSC:32106018795846

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Numerical Methods for Roots of Polynomials Excerpt :

This book (along with volume 2 covers most of the traditional methods for polynomial root-finding such as Newtons, as well as numerous variations on them invented in the last few decades. Perhaps more importantly it covers recent developments such as Vincents 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. P - 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. P.

Numerical Methods for Roots of Polynomials   Part II Book

Numerical Methods for Roots of Polynomials Part II


  • Author : J.M. McNamee
  • Publisher : Elsevier Inc. Chapters
  • Release Date : 2013-07-19
  • Genre: Mathematics
  • Pages : 728
  • ISBN 10 : 9780128077030

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Numerical Methods for Roots of Polynomials Part II Excerpt :

We consider proofs that every polynomial has one zero (and hence n) in the complex plane. This was proved by Gauss in 1799, although a flaw in his proof was pointed out and fixed by Ostrowski in 1920, whereas other scientists had previously made unsuccessful attempts. We give details of Gauss’ fourth (trigonometric) proof, and also more modern proofs, such as several based on integration, or on minimization. We also treat the proofs that polynomials of degree 5 or more cannot in general be solved in terms of radicals. We define groups and fields, the set of congruence classes mod p (x), extension fields, algebraic extensions, permutations, the Galois group. We quote the fundamental theorem of Galois theory, the definition of a solvable group, and Galois’ criterion (that a polynomial is solvable by radicals if and only if its group is solvable). We prove that for the group is not solvable. Finally we mention that a particular quintic has Galois group , which is not solvable, and so the quintic cannot be solved by radicals.

Introduction to Precise Numerical Methods Book

Introduction to Precise Numerical Methods


  • Author : Oliver Aberth
  • Publisher : Elsevier
  • Release Date : 2007-04-11
  • Genre: Mathematics
  • Pages : 272
  • ISBN 10 : 008047120X

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Introduction to Precise Numerical Methods Excerpt :

Precise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed. The book also provides exercises which illustrate points from the text and references for the methods presented. · Clearer, simpler descriptions and explanations of the various numerical methods · Two new types of numerical problems; accurately solving partial differential equations with the included software and computing line integrals in the complex plane.

Numerical Methods for Nonlinear Engineering Models Book

Numerical Methods for Nonlinear Engineering Models


  • Author : John R. Hauser
  • Publisher : Springer Science & Business Media
  • Release Date : 2009-03-24
  • Genre: Technology & Engineering
  • Pages : 1013
  • ISBN 10 : 9781402099205

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Numerical Methods for Nonlinear Engineering Models Excerpt :

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.

Numerical Methods for Roots of Polynomials   Part II Book

Numerical Methods for Roots of Polynomials Part II


  • Author : J.M. McNamee
  • Publisher : Elsevier Inc. Chapters
  • Release Date : 2013-07-19
  • Genre: Mathematics
  • Pages : 728
  • ISBN 10 : 9780128077016

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Numerical Methods for Roots of Polynomials Part II Excerpt :

First we consider the Jenkins–Traub 3-stage algorithm. In stage 1 we defineIn the second stage the factor is replaced by for fixed , and in the third stage by where is re-computed at each iteration. Then a root. A slightly different algorithm is given for real polynomials. Another class of methods uses minimization, i.e. we try to find such that is a minimum, where . At this minimum we must have , i.e. . Several authors search along the coordinate axes or at various angles with them, while others move along the negative gradient, which is probably more efficient. Some use a hybrid of Newton and minimization. Finally we come to Lin and Bairstow’s methods, which divide the polynomial by a quadratic and iteratively reduce the remainder to 0. This enables us to find pairs of complex roots using only real arithmetic.