- Write your own implementation of the adaptive integrator to solidify your understanding.
- What was the name of the function type that the adaptive integrator made use of?
- What makes this type of function special? (its defining characteristic)?
- How does the error of a Monte Carlo (MC) integrator decrease with increasing samples?
- What is the purpose of the majorizing function or curve when using MC integration?
- Write a code to integrate a polynomial using MC. Compare your result to the
quad function.
- A code doing this is provided with the notes, but see if you can do it to test your understanding of the basic principles.
- Outline the key steps
- (like, you have to select a point in the plane, that takes two random numbers, one for x and one for y. Then evaluate the function. Is the point above or below? If below, it’s a hit. Then the integral is the ratio of the hits to the total points multiplied by the area of the reference rectangle.)
- But make sure you understand the what is happening at this level of description, and that you can give this description yourself without reading it. Test it out with a partner (I’m looking at the couple on the back row ;-)