Notes on Computational Methods
This page is an archive of lecture notes and slides that I created mostly when I was teaching at the University of Illinois, Urbana-Champaign (UIUC). Naturally, since the materials are old (most notes were written in 2006-2007), and there are so many textbooks on numerical mathods written since the days I was teaching, I am not sure about the value of these notes. But I still hear nice words about these notes (thanks!), so I leave them here. I am hoping to create my own textbook based on the materials here and other things I learned since my days at UIUC some day.
Numerical Methods
Numerical differentiation [DL]
Numerical optimization (one-dimensional) [DL]
Numerical integration: Gaussian quadrature [DL]
Numerical integration: Newton-Coates quadrature [DL]
Numerical integration: Applications for quantitative macroeconomics [DL]
Function approximation: Finite element methods [DL]
Function approximation: Weighted residual methods [DL]
Function approximation: Chebyshev regression [DL]
Approximating AR(1) process [DL]
Dynamic Programming
Practical introduction to dynamic programming [DL]
Neoclassical Growth Model
Introduction to solving neoclassical growth model [DL]
Solving neoclassical growth model using discretization [DL]
Solving neoclassical growth model using finite element method [DL]
Solving neoclassical growth model using Chebyshev regression [DL]
Real Business Cycle (RBC) Model
Solving RBC model using linear-quadratic (LQ) approximation [DL]
Solving RBC model using log-linearization and Blanchard-Kahn method [DL]
Solving RBC model using log-linearization and method of undetermined coefficients [DL]
Heterogeneous-Agent Model in Steady State (Aiyagari Model)
How to store type distribution [DL]
Solving Aiyagari model [DL]
Solving Aiyagari model with labor-leisure choice and fiscal policy [DL]
Heterogeneous-Agent Model with Aggregate Shocks (Krusell-Smith Model)
Solving the baseline Krusell-Smith model [DL]
Solving Krusell-Smith model with labor-leisure choice
Solving Krusell-Smith model with portfolio choice
Heterogeneous-Agent Model with Endogenous Debt and Default
Solving heterogeneous-agent model with equilibrium default
Solving heterogeneous-agent model with endogenous borrowing constriant
Solving the baseline model with sovereign default
Parallel Computing
Slides on practical introduction for MPI (Message Passing Interface) [DL]