Newton's method

In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function


Applications

Minimization and maximization problems

Newton's method can be used to find a minimum or maximum of a function. The derivative is zero at a minimum or maximum, so minima and maxima can be found by applying Newton's method to the derivative


Examples
Consider the problem of finding the square root of a number. There are many methods of computing square roots, and Newton's method is one.
For example, if one wishes to find the square root of 612, this is equivalent to finding the solution to

http://en.wikipedia.org/wiki/Newton's_method

Newton's Method: Example
http://www.youtube.com/watch?v=0H7L1m4_qvs


Bisection methods, Newton/Raphson and comparison
Lec 6 | MIT 6.00 Introduction to Computer Science and Programming, Fall 2008
http://www.youtube.com/watch?v=hVHqs38fPe8

Newton-Raphson Method: Example
http://www.youtube.com/watch?v=lFYzdOemDj8&feature=relmfu

Newton's Method 1
http://www.youtube.com/watch?v=_MQi3WntZqQ&feature=related

4-5 Newton's Method Example I
http://www.youtube.com/watch?v=cGTc70yDG6I&feature=related

4-5 Newton's Method Example II
http://www.youtube.com/watch?v=iht6utERkZo&feature=related


Newton's Method
http://www.youtube.com/watch?v=E24zUEKqgwQ&feature=related


Newton's Method Example Excel
http://www.youtube.com/watch?v=5ZRjUdjlVoU

Newton's method in C++
http://www.youtube.com/watch?v=dfg9rVl_Tgc&feature=related


Newton's method in java
http://www.youtube.com/watch?v=BLFkHOeaVMY