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May 13th, 2012, 01:39 PM   #1
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newton's method?

can someone show me what newton method is? thank you

Apply Newton’s method to the equation 1/x?a = 0 to derive the following
reciprocal algorithm:
xn+1 = 2xn ? ax2n

http://www.texify.com/img/%5CLARGE%5...%5E%7B2%7D.gif

(which enables a computer to find reciprocals without actually dividing).
Then use this algorithm to compute 1/1.6984 correct to five decimal places.
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May 13th, 2012, 03:26 PM   #2
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Re: newton's method?

We are given:



We compute:



Newtons method gives us the recursion:



Can you proceed to get the required approximation?
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May 13th, 2012, 03:39 PM   #3
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Re: newton's method?

not quiet, first time i learn about this, what to do next?
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May 13th, 2012, 04:54 PM   #4
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Re: newton's method?

???
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May 13th, 2012, 05:53 PM   #5
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Re: newton's method?

What you do is make an initial guess, which is . Then you use the formula to get which you then use to get and so on. As you progress you find converges to the value you are seeking.

So, with:

and (you could begin with any positive initial guess) we have:









Since the last two approximations agree to six places, the approximation rounded to five places is:

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May 13th, 2012, 07:16 PM   #6
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Re: newton's method?

Ok .. the question asking for

Then use this algorithm to compute 1/1.6984 correct to five decimal places.

why a=1.6984
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May 13th, 2012, 07:22 PM   #7
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Re: newton's method?

From we find:



where hence:

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May 13th, 2012, 11:02 PM   #8
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Re: newton's method?

yes! this is good
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