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Numerical Analysis

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Author(s): G. Moore, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part IB Lecture Notes
Publisher: University of Cambridge
Year: 2016

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied

Introduction
Polynomial interpolation
The interpolation problem
The Lagrange formula
The Newton formula
A useful property of divided differences
Error bounds for polynomial interpolation
Orthogonal polynomials
Scalar product
Orthogonal polynomials
Three-term recurrence relation
Examples
Least-squares polynomial approximation
Approximation of linear functionals
Linear functionals
Gaussian quadrature
Expressing errors in terms of derivatives
Ordinary differential equations
Introduction
One-step methods
Multi-step methods
Runge-Kutta methods
Stiff equations
Introduction
Linear stability
Implementation of ODE methods
Local error estimation
Solving for implicit methods
Numerical linear algebra
Triangular matrices
LU factorization
A = LU for special A
Linear least squares