Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Methods of Approximation

Date: 7/31/96 at 14:7:48
From: Albert Nicorgua
Subject: Methods of Approximation


My teacher used Newton's Method of Approximation to solve "Y to the 
power of Y = 25."  Do you know of another way to solve the 
above equation?

--Thanks, Andy

Date: 9/1/96 at 18:5:51
From: Doctor Jerry
Subject: Re: Methods of Approximation

You wish to solve the equation x^x-25=0.  By Newton's Method, I obtain

Another method is called the Bisection Method.  Suppose you want to 
find a zero of a continous function f(x). The idea of the Bisection 
Method is that if f has a xero in an interval [a,b] with midpoint m, 
then f must have a zero in either the left or right half of [a,b].  If 
we choose the first interval so that f(a)*f(b)<0 and let h=m-a, then 
if f(m-h)*f(m)>0, replace the interval [a,b] = [m-h,m+h] by [m,m+h]; 
otherwise, replace [m-h,m+h] by [m-h,m].

Repeat this algorithm until the containing interval is sufficiently 

This method is not as fast as Newton's Method, but can be applied to 
any continuous function, not just differentiable functions.

For the function f(x) = x^x-25, here are a few results. Take the 
intial interval to be [2.5,3.5].  So m=3 and h=0.5.

Successive function values, values of m, and h are




You can see that the midpoints are approaching 2.96...

-Doctor Jerry,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
Associated Topics:
High School Calculus

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994-2015 The Math Forum