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significant digits in NMinimize

Yaj Bhattacharya
Posted 11 years ago

I am trying to get more significant digists (up to 8 or 10) for the following expression and for the value of $b$ where it is minimum,

NMinimize[{(-((4 $\alpha$b$^3$)/(2 b+$\mu$)^$2$)+(64 b$^5$ (6 b + 4 b$^3$ - 16 b$^5$+ (3 Sqrt[1/$b^2$] b $\pi$)/Sqrt[1-b$^2$]-(6 ArcSin[b])/Sqrt[1-$b^2$]))/((96 b$^5$-96 $b^7$) $\pi$))/(1+b$^2$), 0<=b<=0.99999999999},{b}, AccuracyGoal->20] /. { $\alpha$-> 0.05 , $\mu$-> 0.01}

The result is {1.99975, {b -> 0.0227689}}

How can I get some more significant digits?
POSTED BY: Yaj Bhattacharya
4 Replies
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Try to code it neatly, and first do the substitution to make it a lot easier. In addition, change the substitutions to exact fraction:

func=(-((4alpha b^3)/(2 b+mu)^2)+(64 b^5 (6 b+4 b^3-16 b^5+(3 Sqrt[1/b^2] b Pi)/Sqrt[1-b^2]-(6 ArcSin[b])/Sqrt[1-b^2]))/((96 b^5-96 b^7)(Pi)))/(1+b^2);
func=func/.{alpha->1/20,mu->1/100}//Simplify
NMinimize[{func,0<=b<1},{b},AccuracyGoal->40,WorkingPrecision->40]
POSTED BY: Sander Huisman
POSTED BY: Yaj Bhattacharya

Tried formatting it for the forum, the actual input would be

NMinimize[{(-((4alphab^3)/(2 b + mu)^2) + (64 b^5 (6 b + 4 b^3 - 16 b^5 + (3 Sqrt[1/b^2] b [Pi])/ Sqrt[1 - b^2] - (6 ArcSin[b])/Sqrt[1 - b^2]))/((96 b^5 - 96 b^7) [Pi]))/(1 + b^2), 0 <= b <= 0.99999999999}, {b}, AccuracyGoal -> 20] /. {alpha -> 0.05 , mu -> 0.01}
POSTED BY: Yaj Bhattacharya
POSTED BY: Yaj Bhattacharya
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