Implied Volatility from Black-Scholes price

Dan Stefanica and Rados Radoicic propose a quite good initial guess in their very recent paper An Explicit Implied Volatility Formula. Their formula is simple, fast to compute and results in an implied volatility guess with a relative error of less than 10%. It is more robust than the rational fraction from Minquiang Li: his rational fraction is only valid for a fixed range of strikes and maturities. The new approximation is mathematically proved accurate across all strikes and all maturities.