Bisection Methods Newton/Raphson


 

 

 


School: MIT
 
Lecture Title: Bisection Methods Newton/Raphson
 
Lecture Summary:
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.

x : f(x) = 0 \,.

The Newton–Raphson method in one variable is implemented as follows:

The method starts with a function f defined over the real numbers x, the function’s derivative f’, and an initial guess x0 for a root of the function f. If the function satisfies the assumptions made in the derivation of the formula and the initial guess is close, then a better approximation x1 is

x_{1} = x_0 – \frac{f(x_0)}{f'(x_0)} \,.

Geometrically, (x1, 0) is the intersection with the x-axis of the tangent to the graph of f at (x0, f(x0)).
 

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3 thoughts on “Bisection Methods Newton/Raphson”
Anthony Mackey

November 1, 2015

That graph’s line shows a perfect representation of how this whole thing went right over my head.

Lisa

March 8, 2016

Im sure my son will use this a lot while hes flipping burgers.

Alesa

March 9, 2016

Aren’t there calculators that figure this stuff out for us?

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