Programacion

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PREFACE
We thank the faculty and the students of various universities, Engineering colleges and others for sending their suggestions for improving this book. Based on their suggestions, we have made the follwoing changes. (i) New problems have been added and detailed solutions for many problems are given. (ii)C-programs of frequently used numerical methods are given in the Appendix. These programs are written in a simple form and are user friendly. Modifications to these programs can be made to suit individual requirements and also to make them robust. We look forward to more suggestions from the faculty and the students. We are thankful to New Age International Limited for bringing out this Second Edition.New Delhi M.K. Jain S.R.K. Iyengar R.K. Jain

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CONTENTS
Preface 1 TRANSCENDENTAL AND POLYNOMIAL EQUATIONS 1.1 1.2 1.3 1.4 1.5 1.6 1.7 2 (v) 1

Introduction ................................................................................................................... 1 Iterative methods for simple roots............................................................................... 2 Iterative methods for multiple roots ............................................................................ 6 Iterative methods for a system of nonlinear equations .............................................. 7 Complex roots ................................................................................................................ 8 Iterativemethods for polynomial equations ............................................................... 9 Problems and solutions ............................................................................................... 13 71

LINEAR ALGEBRAIC EQUATIONS AND EIGENVALUE PROBLEMS 2.1 2.2 2.3 2.4 2.5 2.6

Introduction................................................................................................................. 71 Direct methods ............................................................................................................ 74 Iteration methods ....................................................................................................... 78 Eigenvalue problems ..................................................................................................80 Special system of equations........................................................................................ 84 Problems and solutions ............................................................................................... 86 144

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INTERPOLATION AND APPROXIMATION 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8

Introduction............................................................................................................... 144 Lagrange and Newton interpolations ...................................................................... 145 Gregory-Newton interpolations ............................................................................... 147 Hermite interpolation ............................................................................................... 150Piecewise and Spline interpolation .......................................................................... 150 Bivariate interpolation ............................................................................................. 153 Approximation ........................................................................................................... 154 Problems and solutions............................................................................................. 158 212

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DIFFERENTIATION AND INTEGRATION 4.1 4.2 4.3 4.4 4.5 4.6

Introduction ............................................................................................................... 212 Numerical differentiation ............................................................................................