Further reading materials for numerical analysis

Chapter 0 Introduction

• Part 2 of Lecture 1
• From numerical analysis to computational sciences by B. Engquist
• N. Trefethen's introduction on numerical analysis
• N. Trefethen's list for classic papers in numerical analysis
• N. Trefethen's prediction for the future of numerical analysis
• N. Trefethen's Talk: Who invent the great algorithms?
• Robust variance computation

Chapter 1 Approximation and interpolation of functions

• Lebesgue constant
• Weierstrass approximation
• Barycentric formula for Lagrange interpolation
• Myths in Polynomial Approximation by Trefethen
• Sparse grid
• Sparse grid: short introduction
• de Boor's B-spline paper
• Error bounds for cubic spline

Chapter 2 Numerical integration

• Quadrature for singular and multidimensional integrals

Chapter 3 Monte Carlo methods

• MCQMC Review by R. Caflish
• MCMC Review by Jordan et al.

Chapter 4 Solving nonlinear system

• History of the Newton-Raphson method
• Homotopy methods for polynomial system
• Nonlinear system: Test problems

Chapter 5 FFT

• Gibbs phenomenon
• FFT--original paper
• Fast multipole algorithm
• Introduction to fast multipole algorithm
• Corrected error estimate in fast Gauss transform

Chapter 6 Numerical ODEs

• Feng Kang Bio.1
• Feng Kang Bio.2
• Symplectic scheme paper by Feng Kang
• Explicit integrators by Eriksson et al
• Fourth order Chebyshev methods by A. Abdulle