Handbook of Numerical Methods for the Solution of Algebraic and Transcendental Equations (eBook)

V. L. Zaguskin (Autor)

eBook Download: PDF

2014 | 1. Auflage
216 Seiten
Elsevier Reference Monographs (Verlag)
978-1-4832-2567-8 (ISBN)

Infos

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.

Inhalt

Front Cover 1
Handbook of Numerical Methods for the Solution of Algebraic and Transcendental Equations 4
Copyright Page 5
Table of Contents 6
FOREWORD 12
AUTHOR'S PREFACE 16
INTRODUCTION 18
CHAPTER I. Initial Information About Polynomials and Transcendental Functions 22
1. Root of a function 22
2. Basic properties of polynomials 22
3. Divisibility of polynomials 23
4. Changing the argument of a polynomial 25
5. Polynomials with real and complex coefficients 27
6. The calculational schemes for the multiplication 
32 
7. Horner's scheme and its application. Calculation 
37 
8. The number of roots and the limits for the roots of 
41 
CHAPTER II. 
48 
1. An approximate number. Absolute and relative 
48 
2. Rounding off 50
3. Operations with approximate numbers 51
4. The error in calculating the value of a polynomial 53
5. The solution of approximate equations 54
6. Plan for the solution of an approximate equation 56
7. Reduction of accuracy when the order of an algebraic Eqution is 
59 
CHAPTER III. 
61 
1. The graphical method 61
2. Approximate determination of the roots of a polynomialby means of Viet's formulae 65
3. The method of N.I.Lobachevskii 68
4. I.Bernoulli's method 94
5. The method of iteration 111
6. Lin's method 114
7. The method of N.V.Paluver 117
8. Comparison of the methods 120
CHAPTER IV. 
123 
1. The method of linear interpolation 123
2. Newton's method 127
3. Berstoi's method 135
4. The method of A.Y.Belostotskii 141
5. Iteration with quadratic convergence 149
6. Methods of improving convergence 154
7. Comparison of the methods 163
CHAPTER V. 
165 
1. Quadratic equations 165
2. Equations of third order 167
3. Equations of fourth order 176
4. Equations of fifth order 178
5. Extraction of roots 178
CHAPTER VI. 
185 
1. The method of elimination 186
2. The graphical method 187
3. The method of iteration 188
4. Newton's method 192
5· The method of steepest descent 196
6. Comparison of methods of solution of simultaneous non-linear equations 197
7. Methods of solution of simultaneous linear 
198 
APPENDIX A: Table for the Solution of Cubic Equations 204
REFERENCES 210
INDEX 214

Produkt-Details

• Erscheint lt. Verlag: 12.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Technik
• ISBN-10: 1-4832-2567-4 / 1483225674
• ISBN-13: 978-1-4832-2567-8 / 9781483225678