Can anyone with math skills that don't suck like mine, solve this?
Posted 26 October 2009 - 10:18 PM
Here is the first derivate function. Anyone know how to solve it? Do I have to solve it iteratively?
0.0625 - 1.5*x^2 + 7.5*x^4 - 14*x^6 + 9x^8 = 0
Posted 26 October 2009 - 10:47 PM
Just using my graphing calculator I found that the roots are at .2357 and .7071 (and corresponding negative ones). The inner root (at .2357) should be easy to refine further using Newton's method if you need more precision. The outer one looks like it's a saddle point, or possibly multiple roots close together, so it will be very hard to do with Newton's method because of the very low slope. You may just have to fall back to bisection there.
Posted 26 October 2009 - 11:05 PM
However, your specific polynomial can be rewritten as a quartic one:
0.0625 - 1.5*z + 7.5*z^2 - 14*z^3 + 9z^4 = 0
z = x^2
Solving for z gives me 0.5 (three times) and 0.055555. Taking their square roots to get x results in 0.70710678 and 0.23570226.
Posted 26 October 2009 - 11:08 PM
Posted 26 October 2009 - 11:17 PM
Ahh OK cool! Thanks again guys. That should get me going.
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