Numerical methods

Related pages: Real analysis • Linear algebra

Resources

Online textbooks:

• Home — Fundamentals of Numerical Computation

Books:

• Numerical Methods for Macroeconomists

§1. Random number generators

• Random number generation - Wikipedia
• RANDOM.ORG - True Random Number Service

§2. Solving nonlinear equations

Julia:

• 10. Optimization and Nonlinear Solvers — Quantitative Economics with Julia

§3. Numerical optimization

Implementations

Julia:

• Optim.jl

• 10. Optimization and Nonlinear Solvers — Quantitative Economics with Julia

Gradient-free methods

Nelder-Mead

• Nelder–Mead method - Wikipedia

Newton's method

• Newton's method in optimization - Wikipedia

Quasi-Newton methods

• Quasi-Newton method - Wikipedia

BFGS

• Broyden–Fletcher–Goldfarb–Shanno algorithm - Wikipedia

• BFGS in a Nutshell: An Introduction to Quasi-Newton Methods | Towards Data Science

DFP

• Davidon–Fletcher–Powell formula - Wikipedia

§4. Numerical differentiation

• Numerical differentiation - Wikipedia

JuliaMATLABPythonR

• FiniteDiff.jl

  This package is for calculating derivatives, gradients, Jacobians, Hessians, etc. numerically.

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§5. Numerical integration

Newton-Cotes formulae

Trapezoid Rule

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Simpson's Rule

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Gaussian Quadrature

Gauss-Legendre Quadrature

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Gauss-Hermite Quadrature

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Monte-Carlo integration

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