Geodesic
Note on Best Approximation of |x|
Canadian mathematical bulletin, Tome 22 (1979) no. 3, pp. 363-366

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In this note the best uniform approximation on [—1,1] to the function |x| by symmetric complex valued linear fractional transformations is determined. This is a special case of the more general problem studied in [1]. Namely, for any even, real valued function f(x) on [-1,1] satsifying 0 = f ( 0 ) ≤ f (x) ≤ f (1) = 1, determine the degree of symmetric approximation and the extremal transformations U whenever they exist. 
Bennett, Colin; Rudnick, Karl; Vaaler, Jeffrey D. Note on Best Approximation of |x|. Canadian mathematical bulletin, Tome 22 (1979) no. 3, pp. 363-366. doi: 10.4153/CMB-1979-046-x
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     author = {Bennett, Colin and Rudnick, Karl and Vaaler, Jeffrey D.},
     title = {Note on {Best} {Approximation} of |x|},
     journal = {Canadian mathematical bulletin},
     pages = {363--366},
     year = {1979},
     volume = {22},
     number = {3},
     doi = {10.4153/CMB-1979-046-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1979-046-x/}
}
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