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Math Help - newton-raphson formula

  1. #1
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    newton-raphson formula

    show that for the function f(x)=2xln*x-1, the newton-raphson formula can be expressed as

    X(n+1)= (X(n)+1/2)/(1+ln*X(n)) , The (n) and (n+1) terms are subscript.



    I have tried using the product rule for f(x) and then some algebraic jiggery but cant even get close to the raphson result.I think I may have made an error in the algebra somewhere.

    Can anyone please give any suggestions???


    Thank you.
    Last edited by bignaughtydog; March 30th 2012 at 05:06 PM.
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  2. #2
    Senior Member BAdhi's Avatar
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    Re: newton-raphson formula

    I guess your equation is f(x)=2xln(x)-1 right?

    then, just use the definition,

    x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}

    f'(x)=2+2ln(x)

    substitute and simplify
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  3. #3
    Junior Member froodles01's Avatar
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    Re: newton-raphson formula

    Yes, using the formula x(n+1) = x(n) - f(x) /f'(x) is the way to go
    f(x) = 2x(n) ln(x(n)) - 1
    f'(x) = 2(ln(x(n)+1)

    substitute these into the formula, multiply terms out & cancel those terms at the top that you can (should be the 2x(n) ln(x(n)) ones)

    At least that's how I did it.
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  4. #4
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    Re: newton-raphson formula

    thank you chaps.i will give it a go : )
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