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Math Help - Numerical Methods - Error propagation and avoiding cancellation

  1. #1
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    Post Numerical Methods - Error propagation and avoiding cancellation

    Simplify (x+sqrt(y))(x-sqrt(y)) & use result to derive a method for avoiding cancellation when solving quadratic equations.

    So (x+sqrt(y))(x-sqrt(y)) simplified is x-y but where do I go from there?
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  2. #2
    Grand Panjandrum
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    Re: Numerical Methods - Error propagation and avoiding cancellation

    Quote Originally Posted by CourtneyMoon View Post
    Simplify (x+sqrt(y))(x-sqrt(y)) & use result to derive a method for avoiding cancellation when solving quadratic equations.

    So (x+sqrt(y))(x-sqrt(y)) simplified is x-y but where do I go from there?
    When you use the quadratic formula the roots are:

    x_1=\frac{-b+\sqrt{b^2-4ac}}{2a}

    x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}

    if 4ac \ll b^2 one of these calculations will result in the subtraction of two nearly equal numbers leading to a loss of precision. This can be avoided by using the simplification you quote, since:

    4a^2 x_1 x_2=b^2-(b^2-4ac)=4ac

    so ....


    CB
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