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Math Help - Numerical analysis

  1. #1
    Nrt
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    Numerical analysis

    Hello, i dont know if its possible but can someone simply explain me how to solve a third degree equation with numerical analysis?
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    Are you looking to find the roots of a third degree polynomial with a numerical method?
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  3. #3
    Nrt
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    Yes.
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    Ok, what methods have you been taught or is this independent learning (happy to suggest some methods), either is fine, do you have a polynomial in particular that needs solving?
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  5. #5
    Nrt
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    Well, i came across some equations in thermodynamics that was solved with this method it seemed eaiser and faster but i couldnt figure it out on my own. they actually showed us about it in calculus ii last year but i didnt pay much attention since i didnt need it untill now. theres no particular polynominal, feel free to give a simple example.

    thanks.
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  6. #6
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    Well as you studied calculus I would suggest using newton's method. It is an iterative process.

    You keep calculating the next value until you see convergence. This value will be the solution.

    For the polynomial \displaystyle f(x)=x^2+2x+7 choose a starting value in the neighbourhood of the solution, in this case \displaystyle x_0=-2 and apply \displaystyle x_{n+1} =x_n-\frac{f(x_n)}{f'(x_n)}

    First find \displaystyle x_1

    \displaystyle x_{1} =x_0-\frac{f(x_0)}{f'(x_0)}= -2-\frac{f(-2)}{f'(-2)}

    What did you get?

    Spoiler:
    \displaystyle x_{1} =-2-\frac{7}{8}=-2.875


    Note this value and find \displaystyle x_2 repeat
    Last edited by pickslides; January 16th 2011 at 04:56 PM. Reason: bad latex
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  7. #7
    Nrt
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    Thank you.
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