I tried c = 15.3559 and get iv = 0.10979904 using both Differential Evolution (DE) and Brent's method in Boost C++.
A benign problem, numerically.
The approach taken in LI 2005 (Taylor series, >>) does not appeal to me at all.
I've lost count of the number of time that 'explicit formula' is mentioned in the text..
The iteration methods for computing IV is definitely applicable in all cases, and accurate. However, since in my cases we are looking for the extreme speed-to reduce the time consumption to less than or equal to 1 BS formula time. This makes most numerical solvers methods inappropriate for us.