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Issue 5.3

FEATURE

REALScience

Integrating with Random Numbers

Issue: 5.3 (March/April 2007)
Author: JC Cruz
Author Bio: JC is a freelance technical writer living in British Columbia. He writes for various publications, and teaches origami at the local district library. He can be reached at: anarakisware@cashette.com
Article Description: No description available.
Article Length (in bytes): 40,871
Starting Page Number: 21
Article Number: 5310
Resource File(s):

Download Icon 5310.zip Updated: 2013-03-11 19:07:59

Related Web Link(s):

http://en.wikipedia.org/wiki/Linear_feedback_shift_register
http://en.wikipedia.org/wiki/Simpson%27s_rule
http://en.wikipedia.org/wiki/Romberg%27s_method

Excerpt of article text...

Today, we will look into the basic concepts of Monte-Carlo integration. We will learn how to implement this algorithm in REALbasic. We will also learn how to use this algorithm to estimate the value of pi. And, as a special treat, we will take a look at another way of generating a random sequence.

A Brief Overview of Numerical Integration

Some computer models are possible only with the use of numerical integration. This group of algorithms used to compute the definite integral of a given function. As shown in Figure 1, the act of integration measures the region enclosed by the function and its bounds.

Most integration algorithms perform their tasks by subdividing the region beneath the curve. Then, they compute the definite integral by adding up all of the subdivisions.

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