# Numerical Analysis Bisection Method Problem

• Jan 18th 2009, 12:18 PM
wvlilgurl
Numerical Analysis Bisection Method Problem
Use the bisection methos to find solutions accurate to within 10^-2 for x^3-7x^2+14x-6=0 for each interval [0,1],[1,3.2],[3.2,4].

I don't know how to find the number of iterations necessary for each interval. Thanks!
• Jan 18th 2009, 12:28 PM
Constatine11
Quote:

Originally Posted by wvlilgurl
Use the bisection methos to find solutions accurate to within 10^-2 for x^3-7x^2+14x-6=0 for each interval [0,1],[1,3.2],[3.2,4].

I don't know how to find the number of iterations necessary for each interval. Thanks!

The interval length is halved at every iteration so after n steps the inteval length is $\displaystyle a\times 2^{-n}$ where $\displaystyle a$ is the initial interval length.

So if we want the $\displaystyle n$-th interval to be less than or equal $\displaystyle 10^{-2}$ we need:

$\displaystyle 10^{-2}\ge a\times 2^{-n}$

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• Jan 19th 2009, 11:12 AM
wvlilgurl
for the interval [0,1] they get 7
for the interval [1,3.2} they get 8

I got the first one at 7 but I cannot get 8 for the second one. DO you knwo how they got 8?
• Jan 19th 2009, 11:32 AM
Constatine11
Quote:

Originally Posted by wvlilgurl
for the interval [0,1] they get 7
for the interval [1,3.2} they get 8

I got the first one at 7 but I cannot get 8 for the second one. DO you knwo how they got 8?

In case 2 we have $\displaystyle a=2.2$, so we seek an integer n such that:

$\displaystyle 10^{-2} \ge 2.2\times 2^{-n}$

which we can use trial and error to find that the smallest integer $\displaystyle n$ such that this holds is $\displaystyle 8$

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• Jan 19th 2009, 11:39 AM
wvlilgurl
still dont get it. I get 6
• Jan 19th 2009, 11:46 AM
Constatine11
Quote:

Originally Posted by Constatine11
In case 2 we have $\displaystyle a=2.2$, so we seek an integer n such that:

$\displaystyle 10^{-2} \ge 2.2\times 2^{-n}$

which we can use trial and error to find that the smallest integer $\displaystyle n$ such that this holds is $\displaystyle 8$

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Put $\displaystyle n=7,\ 2^{-7}\approx 0.0078$ so $\displaystyle 2.2 \times 2^{-7}\approx 0.017>0.01$

Put $\displaystyle n=8,\ 2^{-8}\approx 0.0039$ so $\displaystyle 2.2 \times 2^{-8}\approx0.0086 <0.01$
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