Generalized Karagiannidis–Lioumpas Approximations and Bounds to the Gaussian <i>Q</i>-Function With Optimized Coefficients

We develop extremely tight novel approximations, lower bounds and upper for the Gaussian $Q$ -function offer multiple alternatives coefficient sets thereof, which are optimized in terms of four most relevant criteria: minimax absolute/relative error total error. To minimize maximum, we modify classic Remez algorithm to comply with challenging nonlinearity that pertains proposed expression approximations bounds. On other hand, numerically using quasi-Newton algorithm. The so well matching actual they can be regarded as virtually exact many applications since absolute relative errors 10 −9 xmlns:xlink="http://www.w3.org/1999/xlink">−5 , respectively, reached only ten terms. significant advance accuracy is shown by numerical comparisons key reference cases.