Further reading materials for numerical analysis

Chapter 0 Introduction

• 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?

Chapter 1 Approximation and interpolation of functions

• Lebesgue constant
• Barycentric formula for Lagrange interpolation
• Sparse grid
• de Boor's B-spline paper

Chapter 2 Numerical integration

• Gaussian quadrature error and spectral accuracy
• Quadrature for singular and multidimensional integrals
• Sparse grid integration

Chapter 3 Solving nonlinear system

• Homotopy methods for polynomial system

Chapter 4 FFT

• Gibbs phenomenon
• FFT --original paper
• Fast multiple algorithm
• Introduction to fast multiple algorithm
• Sparse FFT

Chapter 5 Numerical ODE

• 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

Chapter 6 Monte Carlo methods

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