Explore BrainMass
Share

Explore BrainMass

    Cancellation Round-off Error : Numerical Analysis : Confirmation

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    I have numerically solved the following quadratic equation:

    1.002x2 - 11.01x + 0.01265 = 0.

    IS IT POSSIBLE THAT IN THIS INSTANCE EQUATION (2) EQUALS (2A) BELOW:

    If b2 - 4ac >0, the quadratic equation ax2 + bx +c = zero has two real solutions x1, x2 given by the typical:
    (1) x1 = (-b + sqrt(b^2-4ac))/ (2a) , and
    (2) x2 = (-b - sqrt(b^2-4ac))/ (2a)
    By rationalizing the numerator it is also given that:
    (1a) x1 = -2c / ( b + sqrt(b^2 - 4ac))
    (2a) x2 = -2c / ( b - sqrt(b^2 - 4ac))

    IS IT POSSIBLE THAT (2) = (2A) ?

    Using (2), x1 = (11.01 - 11.0077) / (2 * 1.002) = 0.0012

    Using (2a), x2 = (-2 * 0.01265) / (-11.01 -11.0077) = .0012

    If (2) done not equal (2a) what is the relative error of (2a) using 4 digit rounding arithmetic.

    THANK YOU !!

    © BrainMass Inc. brainmass.com October 9, 2019, 8:49 pm ad1c9bdddf
    https://brainmass.com/math/numerical-analysis/cancellation-round-off-error-numerical-analysis-confirmation-163328

    Solution Preview

    Please see the attached file.

    1.002x2 - 11.01x + 0.01265 = 0.

    IS IT POSSIBLE THAT IN THIS INSTANCE EQUATION (2) EQUALS (2A) BELOW:

    If b2 - 4ac >0, the quadratic equation ax2 + bx +c = zero has two real solutions ...

    Solution Summary

    The expert examines cancellations for round-off errors numerical analysis.

    $2.19