Computer oriented numerical methods
V. Rajaraman
- 3rd ed.
- New Delhi: PHI Learning, 2011.
- 196 p. ill.
Preface to the Third Edition 1. Computational Algorithms 1.1 Introduction 1.2 The structure of a computer 1.3 Some examples of algorithms EXERCISES 2 Computer Arithmetic 2.1 Introduction 2.2 Floating point representation of numbers 2.3 Arithmetic operations with normalized floating point numbers 2.4 Consequences of normalized floating point representation of numbers 2.5 Some pitfalls in computing 2.6 Errors in numbers 2.7 Binary representation of numbers 2.8 Conclusions EXERCISES 3. Iterative Methods 3.1 Introduction 3.2 Beginning an iterative method 3.3 The method of successive bisection 3.4 The method of false position 3.5 Newton-Raphson iterative method 3.6 The secant method 3.7 The method of successive approximations 3.8 Comparison of iterative methods 3.9 Solution of polynomial equation 3.10 Solution of simultaneous nonlinear equations EXERCISES 4. Solution of Simultaneous Algebraic Equations 4.1 Introduction 4.2 The Gauss elimination method 4.3 Pivoting 4.4 Illconditioned equations 4.5 Refinement of the solution obtained by Gaussian elimination 4.6 The Gauss-Seidel iterative method 4.7 An algorithm to implement the Gauss-Seidel method 4.8 Comparison of direct and iterative methods EXERCISES 5. Interpolation 5.1 Introduction 5.2 Lagrange interpolation 5.3 Difference tables 5.4 Truncation error in interpolation 5.5 Spline interpolation EXERCISES 6. Least Squares Approximation of Functions 6.1 Introduction 6.2 Linear regression 6.3 Algorithm for linear regression 6.4 Polynomial regression 6.5 Fitting exponential and trigonometric functions EXERCISES 7. Approximation of Functions 7.1 Introduction 7.2 Taylor series representation 7.3 Chebyshev series EXERCISES 8. Differentiation and Integration 8.1 Introduction 8.2 Formulae for numerical differentiation 8.3 Numerical integration 8.4 Simpson's rule 8.5 Errors in integration formulae 8.6 Algorithms for integration of tabulated function ^.7 Algorithms for integrating a known function 8.8 Gaussian quadrature formulae 8.9 Comparison of integration formulae EXERCISES 9. Numerical Solution of Differential Equations 9.1 Introduction 9.2 Euler's method 9.3 Taylor series method 9.4 Runge-Kutta methods 9.5 Runge-Kutta fourth order formula 9.6 Predictor-corrector method 9.7 Higher order differential equations 9.8 Comparison of predictor-corrector and Runge-Kutta methods EXERCISES