I understand from future slides that this technique is super useful for simplifying the actual computation required. However, I am curious as to how the intervals are chosen for the trapezoidal rule. What determines the x0, x1, x2... chosen to estimate the function. Obviously the closer together the x's are, the more accurate, thereby increasing computation cost. What is the balance point of the two?
jlutan
@srikartalluri For the trapezoidal estimate I think the intervals are just evenly spaced depending on the number of how many divisions/samples you take, which is a parameter you can choose. And yes, it would increase computational power with more samples since there would be more terms in the sum but also make the estimate more accurate. For Monte carlo it’s similar except the samples come from a uniform random distribution, which results in varying intervals but also makes it an unbiased estimator.
I understand from future slides that this technique is super useful for simplifying the actual computation required. However, I am curious as to how the intervals are chosen for the trapezoidal rule. What determines the x0, x1, x2... chosen to estimate the function. Obviously the closer together the x's are, the more accurate, thereby increasing computation cost. What is the balance point of the two?
@srikartalluri For the trapezoidal estimate I think the intervals are just evenly spaced depending on the number of how many divisions/samples you take, which is a parameter you can choose. And yes, it would increase computational power with more samples since there would be more terms in the sum but also make the estimate more accurate. For Monte carlo it’s similar except the samples come from a uniform random distribution, which results in varying intervals but also makes it an unbiased estimator.