Computational Economics

  1. Numerical Methods
    1. Root Finding and Equation Solving
      1. Single Equation Methods
        1. Bisection Method
          1. Newton-Raphson Method
            1. Secant Method
              1. Fixed Point Iteration
              2. Systems of Equations
                1. Newton's Method for Systems
                  1. Broyden's Method
                    1. Quasi-Newton Methods
                    2. Convergence Analysis
                      1. Rate of Convergence
                        1. Stopping Criteria
                          1. Error Analysis
                        2. Numerical Optimization
                          1. Unconstrained Optimization
                            1. Gradient Descent Methods
                              1. Steepest Descent
                                1. Step Size Selection
                                  1. Convergence Properties
                                  2. Newton's Method
                                    1. Hessian Matrix Computation
                                      1. Modified Newton Methods
                                      2. Quasi-Newton Methods
                                        1. BFGS Algorithm
                                          1. DFP Algorithm
                                            1. Limited Memory Methods
                                          2. Constrained Optimization
                                            1. Penalty Methods
                                              1. Barrier Methods
                                                1. Sequential Quadratic Programming
                                                  1. Interior Point Methods
                                                  2. Global Optimization
                                                    1. Simulated Annealing
                                                      1. Genetic Algorithms
                                                        1. Particle Swarm Optimization
                                                      2. Numerical Integration
                                                        1. Deterministic Quadrature
                                                          1. Newton-Cotes Formulas
                                                            1. Gaussian Quadrature
                                                              1. Adaptive Quadrature
                                                              2. Monte Carlo Integration
                                                                1. Basic Monte Carlo
                                                                  1. Importance Sampling
                                                                    1. Stratified Sampling
                                                                      1. Variance Reduction Techniques
                                                                      2. Multidimensional Integration
                                                                        1. Product Rules
                                                                          1. Sparse Grids
                                                                            1. Quasi-Monte Carlo Methods
                                                                          2. Function Approximation
                                                                            1. Polynomial Approximation
                                                                              1. Lagrange Interpolation
                                                                                1. Newton Interpolation
                                                                                  1. Chebyshev Polynomials
                                                                                    1. Orthogonal Polynomials
                                                                                    2. Spline Methods
                                                                                      1. Linear Splines
                                                                                        1. Cubic Splines
                                                                                          1. B-Splines
                                                                                            1. Smoothing Splines
                                                                                            2. Spectral Methods
                                                                                              1. Fourier Series
                                                                                                1. Chebyshev Spectral Methods
                                                                                                  1. Collocation Methods
                                                                                                2. Solving Dynamic Models
                                                                                                  1. Discretization Techniques
                                                                                                    1. State Space Discretization
                                                                                                      1. Grid Construction Methods
                                                                                                        1. Curse of Dimensionality
                                                                                                        2. Dynamic Programming
                                                                                                          1. Bellman Equation
                                                                                                            1. Value Function Iteration
                                                                                                              1. Policy Function Iteration
                                                                                                                1. Modified Policy Iteration
                                                                                                                2. Projection Methods
                                                                                                                  1. Galerkin Methods
                                                                                                                    1. Collocation Methods
                                                                                                                      1. Basis Function Selection
                                                                                                                      2. Perturbation Methods
                                                                                                                        1. Linear Approximation
                                                                                                                          1. Higher-Order Perturbations
                                                                                                                            1. Local versus Global Solutions

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                                                                                                                        3. Programming Fundamentals

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                                                                                                                        5. Simulation Methods