Numerical Methods for Roots of Polynomials - Part II
Numerical Methods for Roots of Polynomials - Part II

Author: J.M. McNamee

Publisher: Newnes

Published: 2013-07-19

Total Pages: 749

ISBN-13: 008093143X

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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 I
Numerical Methods for Roots of Polynomials - Part I

Author: J.M. McNamee

Publisher: Elsevier

Published: 2007-08-17

Total Pages: 354

ISBN-13: 0080489478

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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

Numerically Solving Polynomial Systems with Bertini
Numerically Solving Polynomial Systems with Bertini

Author: Daniel J. Bates

Publisher: SIAM

Published: 2013-11-08

Total Pages: 372

ISBN-13: 1611972698

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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.

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: Elsevier

Published: 2014-05-12

Total Pages: 216

ISBN-13: 1483225674

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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 Algorithms
Numerical Algorithms

Author: Justin Solomon

Publisher: CRC Press

Published: 2015-06-24

Total Pages: 400

ISBN-13: 1482251892

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Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig

Scientific Computing
Scientific Computing

Author: Michael T. Heath

Publisher: SIAM

Published: 2018-11-14

Total Pages: 587

ISBN-13: 1611975573

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This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results.? In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include pointers to Python software and the Chebfun package, expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and the availability of about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems.

Polynomial Root-finding and Polynomiography
Polynomial Root-finding and Polynomiography

Author: Bahman Kalantari

Publisher: World Scientific

Published: 2009

Total Pages: 492

ISBN-13: 9812700595

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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.

Algorithms and Complexity
Algorithms and Complexity

Author: Marios Mavronicolas

Publisher: Springer Nature

Published: 2023-04-24

Total Pages: 412

ISBN-13: 3031304489

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This book constitutes the refereed proceedings of the 13th International Conference on Algorithms and Complexity, CIAC 2023, which took place in Larnaca, Cyprus, during June 13–16, 2023. The 25 full papers included in this book were carefully reviewed and selected from 49 submissions. They cover all important areas of research on algorithms and complexity such as algorithm design and analysis; sequential, parallel and distributed algorithms; data structures; computational and structural complexity; lower bounds and limitations of algorithms; randomized and approximation algorithms; parameterized algorithms and parameterized complexity classes; smoothed analysis of algorithms; alternatives to the worst-case analysis of algorithms (e.g., algorithms with predictions), on-line computation and competitive analysis, streaming algorithms, quantum algorithms and complexity, algorithms in algebra, geometry, number theory and combinatorics, computational geometry, algorithmic game theory and mechanism design, algorithmic economics (including auctions and contests), computational learning theory, computational biology and bioinformatics, algorithmic issues in communication networks, algorithms for discrete optimization (including convex optimization) and algorithm engineering.