May 13th, 2012, 01:39 PM  #1 
Member Joined: May 2012 Posts: 34 Thanks: 0  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. 
May 13th, 2012, 03:26 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: newton's method?
We are given: We compute: Newtons method gives us the recursion: Can you proceed to get the required approximation? 
May 13th, 2012, 03:39 PM  #3 
Member Joined: May 2012 Posts: 34 Thanks: 0  Re: newton's method?
not quiet, first time i learn about this, what to do next?

May 13th, 2012, 04:54 PM  #4 
Member Joined: May 2012 Posts: 34 Thanks: 0  Re: newton's method?
???

May 13th, 2012, 05:53 PM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  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: 
May 13th, 2012, 07:16 PM  #6 
Member Joined: May 2012 Posts: 34 Thanks: 0  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 
May 13th, 2012, 07:22 PM  #7 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: newton's method?
From we find: where hence: 
May 13th, 2012, 11:02 PM  #8 
Member Joined: May 2012 Posts: 34 Thanks: 0  Re: newton's method?
yes! this is good 

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