Computer oriented numerical methods V. Rajaraman

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