Iterative Methods For Simultaneous Inclusion Of Polynomial Zeros
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Iterative Methods For Simultaneous Inclusion Of Polynomial Zeros
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Author : Miodrag Petkovic
language : en
Publisher: Springer
Release Date : 2006-11-14
Iterative Methods For Simultaneous Inclusion Of Polynomial Zeros written by Miodrag Petkovic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The simultaneous inclusion of polynomial complex zeros is a crucial problem in numerical analysis. Rapidly converging algorithms are presented in these notes, including convergence analysis in terms of circular regions, and in complex arithmetic. Parallel circular iterations, where the approximations to the zeros have the form of circular regions containing these zeros, are efficient because they also provide error estimates. There are at present no book publications on this topic and one of the aims of this book is to collect most of the algorithms produced in the last 15 years. To decrease the high computational cost of interval methods, several effective iterative processes for the simultaneous inclusion of polynomial zeros which combine the efficiency of ordinary floating-point arithmetic with the accuracy control that may be obtained by the interval methods, are set down, and their computational efficiency is described. The rate of these methods is of interest in designing a package for the simultaneous approximation of polynomial zeros, where automatic procedure selection is desired. The book is both a text and a reference source for mathematicans, engineers, physicists and computer scientists who are interested in new developments and applications, but the material is also accessible to anyone with graduate level mathematical background and some knowledge of basic computational complex analysis and programming.
Iterative Methods For Simultaneous Inclusion Of Polynomial Zeros
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Author : Miodrag Petkovic
language : en
Publisher:
Release Date : 2014-01-15
Iterative Methods For Simultaneous Inclusion Of Polynomial Zeros written by Miodrag Petkovic and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Inclusion Methods For Nonlinear Problems
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Author : Jürgen Herzberger
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Inclusion Methods For Nonlinear Problems written by Jürgen Herzberger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
This workshop was organized with the support of GAMM, the International Association of Applied Mathematics and Mechanics, on the occasion of J. Herzberger's 60th birthday. GAMM is thankful to him for all the time and work he spent in the preparation and holding of the meeting. The talks presented during the workshop and the papers published in this volume are part of the field of Verification Numerics. The important subject is fostered by GAMM already since a number of years, especially also by the GAMM FachausschuB (special interest group) "Rechnerarithmetik und Wissenschaft liches Rechnen". GiHz Alefeld Karlsruhe, Dezember 2001 (President of GAMM) Preface At the end of the year 2000, about 23 scientists from many countries gathered in the beautiful city of Munich on the occasion of the International GAMM Workshop on "Inclusion Methods for Nonlinear Problems with Applications in Engineering, Economics and Physics" from December 15 to 18. The purpose of this meeting was to bring together representatives of research groups from Austria, Bulgaria, China, Croatia, Germany, Japan, Russia, Ukraine and Yugoslavia who in a wider sense work in the field of calculating numerical solutions with error-bounds. Most of those participants have already known each other from earlier occasions or closely cooperated in the past. Representatives from three Academies of Sciences were among the speakers of this conference: from the Bulgarian Academy, the Russian Academy and the Ukrainian Academy of Sciences.
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
Multipoint Methods For Solving Nonlinear Equations
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Author : Miodrag Petkovic
language : en
Publisher: Academic Press
Release Date : 2012-12-31
Multipoint Methods For Solving Nonlinear Equations written by Miodrag Petkovic and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-31 with Technology & Engineering categories.
This book is the first on the topic and explains the most cutting-edge methods needed for precise calculations and explores the development of powerful algorithms to solve research problems. Multipoint methods have an extensive range of practical applications significant in research areas such as signal processing, analysis of convergence rate, fluid mechanics, solid state physics, and many others. The book takes an introductory approach in making qualitative comparisons of different multipoint methods from various viewpoints to help the reader understand applications of more complex methods. Evaluations are made to determine and predict efficiency and accuracy of presented models useful to wide a range of research areas along with many numerical examples for a deep understanding of the usefulness of each method. This book will make it possible for the researchers to tackle difficult problems and deepen their understanding of problem solving using numerical methods. Multipoint methods are of great practical importance, as they determine sequences of successive approximations for evaluative purposes. This is especially helpful in achieving the highest computational efficiency. The rapid development of digital computers and advanced computer arithmetic have provided a need for new methods useful to solving practical problems in a multitude of disciplines such as applied mathematics, computer science, engineering, physics, financial mathematics, and biology. - Provides a succinct way of implementing a wide range of useful and important numerical algorithms for solving research problems - Illustrates how numerical methods can be used to study problems which have applications in engineering and sciences, including signal processing, and control theory, and financial computation - Facilitates a deeper insight into the development of methods, numerical analysis of convergence rate, and very detailed analysis of computational efficiency - Provides a powerful means of learning by systematic experimentation with some of the many fascinating problems in science - Includes highly efficient algorithms convenient for the implementation into the most common computer algebra systems such as Mathematica, MatLab, and Maple
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.
Whereas Newton’s method involves only the first derivative, methods discussed in this chapter involve the second or higher. The “classical” methods of this type (such as Halley’s, Euler’s, Hansen and Patrick’s, Ostrowski’s, Cauchy’s and Chebyshev’s) are all third order with three evaluations, so are slightly more efficient than Newton’s method. Convergence of some of these methods is discussed, as well as composite variations (some of which have fairly high efficiency). We describe special methods for multiple roots, simultaneous or interval methods, and acceleration techniques. We treat Laguerre’s method, which is known to be globally convergent for all-real-roots. The Cluster-Adapted Method is useful for multiple or near-multiple roots. Several composite methods are discussed, as well as methods using determinants or various types of interpolation, and Schroeder’s method.
Numerical Analysis
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Author : Walter Gautschi
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-06
Numerical Analysis written by Walter Gautschi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-06 with Mathematics categories.
Revised and updated, this second edition of Walter Gautschi's successful Numerical Analysis explores computational methods for problems arising in the areas of classical analysis, approximation theory, and ordinary differential equations, among others. Topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible, while subjects requiring a higher level of technicality are referenced in detailed bibliographic notes at the end of each chapter. Readers are thus given the guidance and opportunity to pursue advanced modern topics in more depth. Along with updated references, new biographical notes, and enhanced notational clarity, this second edition includes the expansion of an already large collection of exercises and assignments, both the kind that deal with theoretical and practical aspects of the subject and those requiring machine computation and the use of mathematical software. Perhaps most notably, the edition also comes with a complete solutions manual, carefully developed and polished by the author, which will serve as an exceptionally valuable resource for instructors.
Analysis Approximation Optimization Computation And Applications
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Author : Marija P. Stanić
language : en
Publisher: Springer Nature
Release Date : 2025-07-14
Analysis Approximation Optimization Computation And Applications written by Marija P. Stanić and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-14 with Mathematics categories.
This contributed volume is dedicated to Academician Gradimir V. Milovanović on his 75th birthday and contains recent results in the fields of approximation theory, numerical analysis, mathematical analysis, optimization theory, and various applications of an interdisciplinary character. Most of these results were presented in person during an International Conference “Analysis, Approximations and Applications" (AAA2023), organized by the Faculty of Science, University of Kragujevac in Vrnjačka Banja, Serbia (June 21-24, 2023). This book is intended for researchers and students of mathematics and other computational and applied sciences. This book provides surveys of state of the art results in the fields of Extremal Problems, Optimization and Calculus of Variations; Orthogonal Systems and Quadrature Formulas; Differential and Integral Equations, Integral Transforms and Operation Calculus; Analytic Number Theory and Special Functions; Real and Complex Functions, Sequences, Series, Approximations and Expansions; Functional Analysis, Operator Theory, Fixed Point Theory and Iterative Processes, as well as in Miscellaneous Applications.
World Congress Of Nonlinear Analysts 92
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Author : V. Lakshmikantham
language : en
Publisher: Walter de Gruyter
Release Date : 2011-11-14
World Congress Of Nonlinear Analysts 92 written by V. Lakshmikantham and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-14 with Mathematics categories.
No detailed description available for "World Congress of Nonlinear Analysts '92".
Point Estimation Of Root Finding Methods
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Author : Miodrag Petkovic
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-29
Point Estimation Of Root Finding Methods written by Miodrag Petkovic and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-29 with Mathematics categories.
This book sets out to state computationally verifiable initial conditions for predicting the immediate appearance of the guaranteed and fast convergence of iterative root finding methods. Attention is paid to iterative methods for simultaneous determination of polynomial zeros in the spirit of Smale's point estimation theory, introduced in 1986. Some basic concepts and Smale's theory for Newton's method, together with its modifications and higher-order methods, are presented in the first two chapters. The remaining chapters contain the recent author's results on initial conditions guaranteing convergence of a wide class of iterative methods for solving algebraic equations. These conditions are of practical interest since they depend only on available data, the information of a function whose zeros are sought and initial approximations. The convergence approach presented can be applied in designing a package for the simultaneous approximation of polynomial zeros.