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Handbook of numerical methods for the solution of algebraic and transcendental equations

Author: V L Zaguskin
Publisher: New York : Pergamon Press, 1961.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Zaguskin, V.L.
Handbook of Numerical Methods for the Solution of Algebraic and Transcendental Equations.
New York : Pergamon Press, 1961
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: V L Zaguskin
ISBN: 9781483225678 1483225674
OCLC Number: 898772086
Description: 1 online resource (216 pages)
Contents: Front Cover; Handbook of Numerical Methods for the Solution of Algebraic and Transcendental Equations; Copyright Page; Table of Contents; FOREWORD; AUTHOR'S PREFACE; INTRODUCTION; CHAPTER I. Initial Information About Polynomials and Transcendental Functions; 1. Root of a function; 2. Basic properties of polynomials; 3. Divisibility of polynomials; 4. Changing the argument of a polynomial; 5. Polynomials with real and complex coefficients; 6. The calculational schemes for the multiplicationand division of polynomials. 7. Horner's scheme and its application. Calculationof the value of a polynomial8. The number of roots and the limits for the roots ofa polynomial; CHAPTER II. Operations with Approximate Numbers; 1. An approximate number. Absolute and relativeerrors; 2. Rounding off; 3. Operations with approximate numbers; 4. The error in calculating the value of a polynomial; 5. The solution of approximate equations; 6. Plan for the solution of an approximate equation; 7. Reduction of accuracy when the order of an algebraic Eqution isLowered; CHAPTER III. Methods for Approximate Determination of Roots. 1. The graphical method2. Approximate determination of the roots of a polynomialby means of Viet's formulae; 3. The method of N.I. Lobachevskii; 4. I. Bernoulli's method; 5. The method of iteration; 6. Lin's method; 7. The method of N.V. Paluver; 8. Comparison of the methods; CHAPTER IV. Methods of Making More Accurate Roots Already Found; 1. The method of linear interpolation; 2. Newton's method; 3. Berstoi's method; 4. The method of A.Y. Belostotskii; 5. Iteration with quadratic convergence; 6. Methods of improving convergence; 7. Comparison of the methods. CHAPTER V. Solution of Equations of Low Orders and Extraction of Roots1. Quadratic equations; 2. Equations of third order; 3. Equations of fourth order; 4. Equations of fifth order; 5. Extraction of roots; CHAPTER VI. Solution of Simultaneous Equations; 1. The method of elimination; 2. The graphical method; 3. The method of iteration; 4. Newton's method; 5· The method of steepest descent; 6. Comparison of methods of solution of simultaneous non-linear equations; 7. Methods of solution of simultaneous linearequations; APPENDIX A: Table for the Solution of Cubic Equations; REFERENCES; INDEX.
Other Titles: Spravochnik po chislennym metodam reshnii︠a︡ algebraicheskikh i trant︠s︡endentnykh uraveniĭ.
Responsibility: by V.L. Zaguskin ; Translated from the Russian by G.O. Harding.

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