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Topic: Given an iterative equation to solve an equation
Replies: 2   Last Post: Jan 20, 2013 1:27 PM

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Roger Stafford

Posts: 5,929
Registered: 12/7/04
Re: Given an iterative equation to solve an equation
Posted: Jan 20, 2013 1:27 PM
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"Jacob" wrote in message <kdf58n$958$>...
> An iterative equation for solving the equation x^2-x-1=0 is given by
> x(r+1)=1+(1/x(r)) for r=0,1,2,...
> Given x0=2, write a Matlab script to solve the equation. Sufficient accuracy is obtained when abs(x(r+1)-x(r))<.0005.
> I am a new to Matlab and I am having a hard time really even starting this problem. I was thinking that using some sort of loop until the accuracy condition is met would work. Any help would be much appreciated.
> Thanks in advance,
> Jacob

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You will find that matlab's 'while' function is very useful for a problem like yours using the inequality you have stated. I tried it on my computer and it took nine trips through the loop before the inequality was satisfied.

It is important to realize that in general such iterative schemes are not guaranteed to converge to a solution or may be less efficient than other iterations. It all depends on the nature of the iterative formula. In this problem for example there is a second root to the quadratic equation but this iterative scheme apparently diverges away from it rather than toward it.

There is another iterative formula which is derived from the Newton-Raphson method that will converge much faster

x(n+1) = (x(n)^2+1)/(2*x(n)-1)

and is capable of converging on either root depending on the initial value used.

Roger Stafford

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