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.
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.
Download or read book Numerical Methods for Roots of Polynomials Part II written by J.M. McNamee and published by Newnes. This book was released on 2013-07-19 with total page 749 pages. Available in PDF, EPUB and Kindle. Book 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
Download or read book Initial Approximations and Root Finding Methods written by Nikolay N. Kyurkchiev and published by . This book was released on 1998 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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
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 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 94 pages. Available in PDF, EPUB and Kindle. Book 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.
Download or read book Numerical Methods written by Rajesh Kumar Gupta and published by Cambridge University Press. This book was released on 2019-05-09 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in an easy-to-understand manner, this comprehensive textbook brings together both basic and advanced concepts of numerical methods in a single volume. Important topics including error analysis, nonlinear equations, systems of linear equations, interpolation and interpolation for Equal intervals and bivariate interpolation are discussed comprehensively. The textbook is written to cater to the needs of undergraduate students of mathematics, computer science, mechanical engineering, civil engineering and information technology for a course on numerical methods/numerical analysis. The text simplifies the understanding of the concepts through exercises and practical examples. Pedagogical features including solved examples and unsolved exercises are interspersed throughout the book for better understanding.
Download or read book Polynomial Root Finding and Polynomiography written by Bahman Kalantari and published by World Scientific. This book was released on 2009 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Some Remarks on a Root Finding Method Using Pade Approximation written by G. Claessens and published by . This book was released on 1977 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Graphical Demonstration of Root Finding Methods written by Christopher D. Costello and published by . This book was released on 1987 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods for Science and Engineering written by B. Ravindra Reddy and published by BSP Books . This book was released on 2024-08-01 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: About the Book: Numerical Methods is the go-to textbook for B.Sc and B.Tech students in search of a comprehensive guide to numerical analysis. This self-contained classroom text offers an in-depth exploration of key topics such as errors, difference operators, and interpolation with both equal and unequal intervals. With detailed explanations of methods for solving linear algebraic and transcendental equations, numerical integration, differentiation, and ordinary differential equations. Additional topics covered in this text include central difference interpolation formulas, inverse interpolation, and the Guass-Jacobi and Gauss Seidel methods. Whether you are a student or a professional in the field of numerical analysis, Numerical Methods provides the solid foundation you need to succeed. This book is an essential resource for students seeking to master the principles and techniques of numerical analysis.Contents: 1. Errors in Numerical Calculations 2. Solving Algebraic and Transcendental Equations 3. Differential Operators 4. Interpolation with Equal Intervals 5. Matrices, Characteristic Equation, Eigen Values and Eigen Vector 6. Central difference Interpolation Formulae 7. Numerical Differentiation 8. Numerical Integration 9. Solution of Ordinary Differential Equations 10. Inverse Interpolation 11. Curve Fitting 12. Solving of a System of Linear Equations and Matrices
Download or read book Elementary Numerical Methods written by M. J. Jamieson and published by . This book was released on 1983 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Solutions Manual to accompany An Introduction to Numerical Methods and Analysis written by James F. Epperson and published by John Wiley & Sons. This book was released on 2021-09-15 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Third Edition An Introduction to Numerical Methods and Analysis helps students gain a solid understanding of a wide range of numerical approximation methods for solving problems of mathematical analysis. Designed for entry-level courses on the subject, this popular textbook maximizes teaching flexibility by first covering basic topics before gradually moving to more advanced material in each chapter and section. Throughout the text, students are provided clear and accessible guidance on a wide range of numerical methods and analysis techniques, including root-finding, numerical integration, interpolation, solution of systems of equations, and many others. This fully revised third edition contains new sections on higher-order difference methods, the bisection and inertia method for computing eigenvalues of a symmetric matrix, a completely re-written section on different methods for Poisson equations, and spectral methods for higher-dimensional problems. New problem sets—ranging in difficulty from simple computations to challenging derivations and proofs—are complemented by computer programming exercises, illustrative examples, and sample code. This acclaimed textbook: Explains how to both construct and evaluate approximations for accuracy and performance Covers both elementary concepts and tools and higher-level methods and solutions Features new and updated material reflecting new trends and applications in the field Contains an introduction to key concepts, a calculus review, an updated primer on computer arithmetic, a brief history of scientific computing, a survey of computer languages and software, and a revised literature review Includes an appendix of proofs of selected theorems and author-hosted companion website with additional exercises, application models, and supplemental resources
Download or read book A First Course in Numerical Analysis written by Anthony Ralston and published by . This book was released on 1965 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods written by M. D. PETALE and published by MANGESH DEVIDASRAO PETALE. This book was released on with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: Purpose of this Book The purpose of this book is to supply lots of examples with details solution that helps the students to understand each example step wise easily and get rid of the college assignments phobia. It is sincerely hoped that this book will help and better equipped the higher secondary students to prepare and face the examinations with better confidence. I have endeavored to present the book in a lucid manner which will be easier to understand by all the engineering students. About the Book According to many streams in engineering course there are different chapters in Engineering Mathematics of the same year according to the streams. Hence students faced problem about to buy Engineering Mathematics special book that covered all chapters in a single book. That’s reason student needs to buy many books to cover all chapters according to the prescribed syllabus. Hence need to spend more money for a single subject to cover complete syllabus. So here good news for you, your problem solved. I made here special books according to chapter wise, which helps to buy books according to chapters and no need to pay extra money for unneeded chapters that not mentioned in your syllabus. PREFACE It gives me great pleasure to present to you this book on A Textbook on “Numerical Methods” of Engineering Mathematics presented specially for you. Many books have been written on Engineering Mathematics by different authors and teachers, but majority of the students find it difficult to fully understand the examples in these books. Also, the Teachers have faced many problems due to paucity of time and classroom workload. Sometimes the college teacher is not able to help their own student in solving many difficult questions in the class even though they wish to do so. Keeping in mind the need of the students, the author was inspired to write a suitable text book providing solutions to various examples of “Numerical Methods” of Engineering Mathematics. It is hoped that this book will meet more than an adequately the needs of the students they are meant for. I have tried our level best to make this book error free.
Download or read book A Study of a Modified Form of Newton s Method for Real Root Approximations written by Philip Sheridan Daulton and published by . This book was released on 1951 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
