Math 170b - Numerical Analysis

Description: Rounding and discretization errors. Calculation of roots of polynomials and nonlinear equations, Interpolation, Approximation of functions.
Instructor: Professor Micheal Griebel (winter 2000)

CHAPTER ONE:- ROOT FINDING FOR NON-LINEAR EQUATIONS [f(x)=0]

1. Bisect method
2. Newton method, rate of convergence
3. Secant method, rate of convergence
4. Regula falsi method
5. Modified Regula falsi method
6. Muller method

CHAPTER TWO:- INTERPOLATION THEORY

1. polynomial interpolation theory
2. Langrange's polynomial interpolations
3. Newton Divided difference
4. Hermite interpolations 5. Cubic Spline (free Spline and Clamped Spline)
6. Trigonometric interpolation

CHAPTER THREE:- APPROXIMATIONS

1. Minmax approximation problem
2. Least-Squares approximation problem (discrete and cont.)
3. Weighted least square problems
4. Legendre polynomials
5. Laguerre polynomials
6. Chebyshev polynomials
7. Orthogonal polynomial (Gram-schmidt ortho)