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!

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- Jan 18th 2009, 12:18 PMwvlilgurlNumerical 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 PMConstatine11
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:

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

. - Jan 19th 2009, 11:12 AMwvlilgurl
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 AMConstatine11
- Jan 19th 2009, 11:39 AMwvlilgurl
*still dont get it. I get 6* - Jan 19th 2009, 11:46 AMConstatine11