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Author : Miodrag Petkovic
Publisher :
ISBN 13 : 9783662211304
Total Pages : 280 pages
Book Rating : 4.2/5 (113 download)
Download or read book Iterative Methods for Simultaneous Inclusion of Polynomial Zeros written by Miodrag Petkovic and published by . This book was released on 2014-01-15 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Miodrag Petkovic
Publisher : Springer
ISBN 13 : 3540481745
Total Pages : 272 pages
Book Rating : 4.5/5 (44 download)
Download or read book Iterative Methods for Simultaneous Inclusion of Polynomial Zeros written by Miodrag Petkovic and published by Springer. This book was released on 2006-11-14 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Nikolay V. Kyurkchiev
Publisher : Wiley-VCH
ISBN 13 :
Total Pages : 224 pages
Book Rating : 4.X/5 (4 download)
Download or read book Initial Approximations and Root Finding Methods written by Nikolay V. Kyurkchiev and published by Wiley-VCH. This book was released on 1998-10-27 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : G.V. Milovanovic
Publisher : Springer Science & Business Media
ISBN 13 : 9401590869
Total Pages : 518 pages
Book Rating : 4.4/5 (15 download)
Download or read book Recent Progress in Inequalities written by G.V. Milovanovic and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the late Professor Dragoslav S. Mitrinovic(1908-1995), one of the most accomplished masters in the domain of inequalities. Inequalities are to be found everywhere and play an important and significant role in almost all subjects of mathematics as well as in other areas of sciences. Professor Mitrinovic used to say: `There are no equalities, even in human life inequalities are always encountered.' This volume provides an extensive survey of the most current topics in almost all subjects in the field of inequalities, written by 85 outstanding scientists from twenty countries. Some of the papers were presented at the International Memorial Conference dedicated to Professor D.S. Mitrinovic, which was held at the University of Nis, June 20-22, 1996. Audience: This book will be of great interest to researchers in real, complex and functional analysis, special functions, approximation theory, numerical analysis and computation, and other fields, as well as to graduate students requiring the most up-to-date results.
Author : Jürgen Herzberger
Publisher : Springer Science & Business Media
ISBN 13 : 3709160332
Total Pages : 247 pages
Book Rating : 4.7/5 (91 download)
Download or read book Inclusion Methods for Nonlinear Problems written by Jürgen Herzberger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Miodrag Petković
Publisher : John Wiley & Sons
ISBN 13 : 9783527401345
Total Pages : 296 pages
Book Rating : 4.4/5 (13 download)
Download or read book Complex Interval Arithmetic and Its Applications written by Miodrag Petković and published by John Wiley & Sons. This book was released on 1998 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present formulas and methods developed using complex interval arithmetic. While most of numerical methods described in the literature deal with real intervals and real vectors, there is no systematic study of methods in complex interval arithmetic. The book fills this gap. Several main subjects are considered: outer estimates for the range of complex functions, especially complex centered forms, the best approximations of elementary complex functions by disks, iterative methods for the inclusion by polynomial zeros including their implementation on parallel computers, the analysis of numerical stability of iterative methods by using complex interval arithmetic and numerical computation of curvilinear integrals with error bounds. Mainly new methods are presented developed over the last years, including a lot of very recent results by the authors some of which have not been published before.
Author : Miodrag Petkovic
Publisher : Academic Press
ISBN 13 : 0123972981
Total Pages : 317 pages
Book Rating : 4.1/5 (239 download)
Download or read book Multipoint Methods for Solving Nonlinear Equations written by Miodrag Petkovic and published by Academic Press. This book was released on 2012-12-31 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : Walter Krämer
Publisher : Springer Science & Business Media
ISBN 13 : 1475764847
Total Pages : 385 pages
Book Rating : 4.4/5 (757 download)
Download or read book Scientific Computing, Validated Numerics, Interval Methods written by Walter Krämer and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scan 2000, the GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics and Interval 2000, the International Conference on Interval Methods in Science and Engineering were jointly held in Karlsruhe, September 19-22, 2000. The joint conference continued the series of 7 previous Scan-symposia under the joint sponsorship of GAMM and IMACS. These conferences have traditionally covered the numerical and algorithmic aspects of scientific computing, with a strong emphasis on validation and verification of computed results as well as on arithmetic, programming, and algorithmic tools for this purpose. The conference further continued the series of 4 former Interval conferences focusing on interval methods and their application in science and engineering. The objectives are to propagate current applications and research as well as to promote a greater understanding and increased awareness of the subject matters. The symposium was held in Karlsruhe the European cradle of interval arithmetic and self-validating numerics and attracted 193 researchers from 33 countries. 12 invited and 153 contributed talks were given. But not only the quantity was overwhelming we were deeply impressed by the emerging maturity of our discipline. There were many talks discussing a wide variety of serious applications stretching all parts of mathematical modelling. New efficient, publicly available or even commercial tools were proposed or presented, and also foundations of the theory of intervals and reliable computations were considerably strengthened.
Author : G. Alefeld
Publisher : Springer Science & Business Media
ISBN 13 : 3709162173
Total Pages : 253 pages
Book Rating : 4.7/5 (91 download)
Download or read book Topics in Numerical Analysis written by G. Alefeld and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains eighteen papers submitted in celebration of the sixty-fifth birthday of Professor Tetsuro Yamamoto of Ehime University. Professor Yamamoto was born in Tottori, Japan on January 4, 1937. He obtained his B. S. and M. S. in mathematics from Hiroshima University in 1959 and 1961, respec tively. In 1966, he took a lecturer position in the Department of Mathematics, Faculty of General Education, Hiroshima University and obtained his Ph. D. degree from Hiroshima University two years later. In 1969, he moved to the Department of Applied Mathematics, Faculty of Engineering, Ehime University as an associate professor and he has been a full professor of the Department of Mathematics (now Department of Mathematical Sciences), Faculty of Science, since 1975. At the early stage of his study, he was interested in algebraic eigen value problems and linear iterative methods. He published some papers on these topics in high level international journals. After moving to Ehime University, he started his research on Newton's method and Newton-like methods for nonlinear operator equations. He published many papers on error estimates of the methods. He established the remarkable result that all the known error bounds for Newton's method under the Kantorovich assumptions follow from the Newton-Kantorovich theorem, which put a period to the race of finding sharper error bounds for Newton's method.
Author : Nur Raidah Salim
Publisher :
ISBN 13 :
Total Pages : 304 pages
Book Rating : 4.:/5 (975 download)
Download or read book Convergence of Interval Symmetric Single-step Method for Simultaneous Inclusion of Real Polynomial Zeros written by Nur Raidah Salim and published by . This book was released on 2012 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Miodrag Petkovic
Publisher : Springer Science & Business Media
ISBN 13 : 3540778500
Total Pages : 222 pages
Book Rating : 4.5/5 (47 download)
Download or read book Point Estimation of Root Finding Methods written by Miodrag Petkovic and published by Springer Science & Business Media. This book was released on 2008-05-29 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : J.M. McNamee
Publisher : Elsevier Inc. Chapters
ISBN 13 : 0128076992
Total Pages : 182 pages
Book Rating : 4.1/5 (28 download)
Download or read book Numerical Methods for Roots of Polynomials - Part II written by J.M. McNamee and published by Elsevier Inc. Chapters. This book was released on 2013-07-19 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : A. Neumaier
Publisher : Cambridge University Press
ISBN 13 : 052133196X
Total Pages : 275 pages
Book Rating : 4.5/5 (213 download)
Download or read book Interval Methods for Systems of Equations written by A. Neumaier and published by Cambridge University Press. This book was released on 1990 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Author : V. Lakshmikantham
Publisher : Walter de Gruyter
ISBN 13 : 3110883236
Total Pages : 4040 pages
Book Rating : 4.1/5 (18 download)
Download or read book World Congress of Nonlinear Analysts '92 written by V. Lakshmikantham and published by Walter de Gruyter. This book was released on 2011-11-14 with total page 4040 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Andrea Cangiani
Publisher : Springer Science & Business Media
ISBN 13 : 3642331343
Total Pages : 811 pages
Book Rating : 4.6/5 (423 download)
Download or read book Numerical Mathematics and Advanced Applications 2011 written by Andrea Cangiani and published by Springer Science & Business Media. This book was released on 2013-01-20 with total page 811 pages. Available in PDF, EPUB and Kindle. Book excerpt: The European Conferences on Numerical Mathematics and Advanced Applications (ENUMATH) are a series of conferences held every two years to provide a forum for discussion of new trends in numerical mathematics and challenging scientific and industrial applications at the highest level of international expertise. ENUMATH 2011 was hosted by the University of Leicester (UK) from the 5th to 9th September 2011. This proceedings volume contains more than 90 papers by speakers of the conference and gives an overview of recent developments in scientific computing, numerical analysis, and practical use of modern numerical techniques and algorithms in various applications. New results on finite element methods, multiscale methods, numerical linear algebra, and finite difference schemes are presented. A range of applications include computational problems from fluid dynamics, materials, image processing, and molecular dynamics.
Author : R. Albrecht
Publisher : Springer Science & Business Media
ISBN 13 : 3709169186
Total Pages : 288 pages
Book Rating : 4.7/5 (91 download)
Download or read book Validation Numerics written by R. Albrecht and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this book give a comprehensive overview on the whole field of validated numerics. The problems covered include simultaneous systems of linear and nonlinear equations, differential and integral equations and certain applications from technical sciences. Furthermore some papers which improve the tools are included. The book is a must for scientists working in numerical analysis, computer science and in technical fields.
Author : J.M. McNamee
Publisher : Elsevier
ISBN 13 : 0080489478
Total Pages : 354 pages
Book Rating : 4.0/5 (84 download)
Download or read book Numerical Methods for Roots of Polynomials - Part I written by J.M. McNamee and published by Elsevier. This book was released on 2007-08-17 with total page 354 pages. Available in PDF, EPUB and Kindle. Book 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
