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Numerical Methods For Roots Of Polynomials Part I

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Numerical Methods For Roots Of Polynomials Part I

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Author : J.M. McNamee
language : en
Publisher: Elsevier
Release Date : 2007-08-17

Numerical Methods For Roots Of Polynomials Part I written by J.M. McNamee and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-17 with Mathematics categories.

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 Part Ii

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Author : J.M. McNamee
language : en
Publisher: Elsevier Inc. Chapters
Release Date : 2013-07-19

Numerical Methods For Roots Of Polynomials Part Ii written by J.M. McNamee and has been published by Elsevier Inc. Chapters this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-19 with Mathematics categories.

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 Ii

DOWNLOAD
Author : J.M. McNamee
language : en
Publisher: Elsevier Inc. Chapters
Release Date : 2013-07-19

Numerical Methods For Roots Of Polynomials Part Ii

DOWNLOAD
Author : J.M. McNamee
language : en
Publisher: Elsevier Inc. Chapters
Release Date : 2013-07-19

This chapter treats several topics, starting with Bernoulli’s method. This method iteratively solves a linear difference equation whose coefficients are the same as those of the polynomial. The ratios of successive iterates tends to the root of largest magnitude. Special versions are used for complex and/or multiple roots. The iteration may be accelerated, and Aitken’s variation finds all the roots simultaneously. The Quotient-Difference algorithm uses two sequences(with a similar one for ). Then, if the roots are well separated, . Special techniques are used for roots of equal modulus. The Lehmer–Schur method uses a test to determine whether a given circle contains a root or not. Using this test we find an annulus which contains a root, whereas the circle does not. We cover the annulus with 8 smaller circles and test which one contains the roots. We repeat the process until a sufficiently small circle is known to contain the root. We also consider methods using integration, such as by Delves–Lyness and Kravanja et al.

Computational Methods In Physics

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Author : Simon Širca
language : en
Publisher: Springer
Release Date : 2018-06-21

Computational Methods In Physics written by Simon Širca and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-21 with Science categories.

This book is intended to help advanced undergraduate, graduate, and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues, as well as optimization of program execution speeds. Numerous examples are given throughout the chapters, followed by comprehensive end-of-chapter problems with a more pronounced physics background, while less stress is given to the explanation of individual algorithms. The readers are encouraged to develop a certain amount of skepticism and scrutiny instead of blindly following readily available commercial tools. The second edition has been enriched by a chapter on inverse problems dealing with the solution of integral equations, inverse Sturm-Liouville problems, as well as retrospective and recovery problems for partial differential equations. The revised text now includes an introduction to sparse matrix methods, the solution of matrix equations, and pseudospectra of matrices; it discusses the sparse Fourier, non-uniform Fourier and discrete wavelet transformations, the basics of non-linear regression and the Kolmogorov-Smirnov test; it demonstrates the key concepts in solving stiff differential equations and the asymptotics of Sturm-Liouville eigenvalues and eigenfunctions. Among other updates, it also presents the techniques of state-space reconstruction, methods to calculate the matrix exponential, generate random permutations and compute stable derivatives.

Numerical Methods For Roots Of Polynomials Part I

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Author : J.M. McNamee
language : en
Publisher: Elsevier Science
Release Date : 2007-08-17

Numerical Methods For Roots Of Polynomials Part I written by J.M. McNamee and has been published by Elsevier Science this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-17 with Mathematics categories.

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.

Scientific Computing

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Author : Michael T. Heath
language : en
Publisher: SIAM
Release Date : 2018-11-14

Scientific Computing written by Michael T. Heath and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-14 with Science categories.

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.

Algorithms And Complexity

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Author : Marios Mavronicolas
language : en
Publisher: Springer Nature
Release Date : 2023-04-24

Algorithms And Complexity written by Marios Mavronicolas and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-24 with Computers categories.

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.

Numerical Methods That Work

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Author : Forman S. Acton
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-07-31

Numerical Methods That Work written by Forman S. Acton and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-31 with Mathematics categories.

Polynomial Root Finding And Polynomiography

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Author : Bahman Kalantari
language : en
Publisher: World Scientific
Release Date : 2009

Polynomial Root Finding And Polynomiography written by Bahman Kalantari and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Computers categories.

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.

Numerical Methods For Roots Of Polynomials Part I

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