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What are the roots of polynomial, x^3 + (12e-6)*x - (e-9)*1.9=0?
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Chapter 11 User Data Recipes. Chapter 12 Data Storage Recipes. They should be There is also a similar error in the real part of the two complex conjugate solutions. The numerical technique I have proposed gives a more precise result. It is a stable successive-division scheme that completely avoids cancellation effects and that bx-12e able to yield a solution to a very high precision. Hayette Gatfaoui. Dear Jeannie, I don't know if it helps but here are my thoughts about your problem.
I think you are looking for real solutions about your problem. Moreover, the bx-12e order derivative is positive whatever x in the real set so that we have an increasing function of x. Hence, there is only one root for your function in the real set.
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As the result, the only solution is to use numerical tools for your computations. I hope this helps you to get a better view Moreover, when you use a software, the accuracy of the obtained result depends on the numerical method that is chosen and also the tolerance level that bx-12e set by default e. By how much do you allow the computations to deviate from the exact 0 value. The Newton-Raphson algorithm is fine for linear problems but not the best for nonlinear ones like yours. Other algorithms such as Davdon-Fletcher-Powell perform conveniently for example. Dear Hayette. I do not agree with you. The Newton-Raphson method is perfectly able to yield a highly accurate solution for the original problem formulated by Jeannie.
This solution yields a residual bx-12e about 6E As to the Davidon-Fletcher-Powell method, it is a quasi-Newton variable-metric method which is generally used in the context of unconstrained optimization problems. Why do you recommend it here to solve a cubic equation? Indeed H. Lehtihet, in the present case, you are right.
Moreover, the shape of the function is so that around the unique real root is bx-12e to be linear close to the change of curvature. So it eases a lot the computations.
The quasi-Newton method was bx-12e simply because in many cases it offers better convergence properties and often better accuracy. Moreover, it will probably be helpful if the future research drives Jeannie towards a polynomial with more than one variable just in case. Actually, there bx-12e a set of interesting articles about the comparison between Newton and Quasi-Newton methods. Bx 12e Driver for Windows 7 32 bit, Windows 7 64 bit, Windows 10, 8, XP. Uploaded on 4/14/, downloaded times, receiving a 92/ rating by "sNSLayoutConstraint:Bxbbfl HII'IN55§BCB[ZBll* lUIRoundedRectButton:BxTlZelSB] (Names: ' ':UIView:Bx" 1 Figure Forgetting to turn off.