EXACT UPPER AND LOWER BOUNDS ON THE DIFFERENCE BETWEEN THE ARITHMETIC AND GEOMETRIC MEANS

@article{Pinelis2015EXACTUA,
title={EXACT UPPER AND LOWER BOUNDS ON THE DIFFERENCE BETWEEN THE ARITHMETIC AND GEOMETRIC MEANS},
author={Iosif Pinelis},
journal={Bulletin of the Australian Mathematical Society},
year={2015},
volume={92},
pages={149 - 158}
}
• I. Pinelis
• Published 1 March 2015
• Mathematics
• Bulletin of the Australian Mathematical Society
Exact upper and lower bounds on the difference between the arithmetic and geometric means are obtained. The inequalities providing these bounds may be viewed, respectively, as a reverse Jensen inequality and an improvement of the direct Jensen inequality, in the case when the convex function is the exponential.
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A Bibliography of Publications about the Arithmetic–Geometric Mean Iteration
(a, b)← ( a+3b 4 , √ ab+b 2 ) [BB89]. 1 [BM88]. 2 [BM88, Gau02, KM10, KM12]. 3 [LR07]. \$49.95 [Ber88]. B [SL98]. D4 [Sol95]. e [Has13b, Has14, YY01]. E6 [Sol95]. E8 [Sol95]. λ [SMY14]. C [CT13a]. μ