Numerical integration: simple deterministic methods in 1D; Monte Carlo integration.

- 1D classical integration methods: trapezoidal rule, Simpson...

- Monte Carlo integration in 1D: "hit or miss" (or "acceptance-rejection"); "sample mean".

- algorithms to improve the efficiency: importance sampling

- Handling errors: variance reduction with (i) average of the averages (ii) block average  

Multidimensional numerical integration: comparison between deterministic and Monte Carlo methods.

Error analysis

- error in classical methods with equispaced abscissas in one and higher dimensions

- comparison with errors in Monte Carlo method

More on 1D numerical integration: Gaussian Quadrature

- Classical 1D integration: Gaussian Quadrature, Ortjogonal polynomials

- Gauss-Legendre quadrature (use of "gauleg" subroutine from Numerical Recipes)

Generalities about the use of Numerical Recipes


References:

- Chapter 1.2 "Numerical quadrature" from "Computational Physics" by Koonin; chapter 8.1-2

- Chapter 11 "Numerical Integration" from "Computer simulation Methods" by Gould-Tobochnik (II ed)


Ultime modifiche: giovedì, 23 marzo 2023, 10:40