A Piecewise Linear Approximation of Log2x with Equal Maximum Errors in All Intervals

In this paper it is shown how to divide the interval [1,2] into n parts so that the uniform linear approximation of log2x in each subinterval has the same maximum error. This error is, in the case n = 4, smaller by a factor of 2.3 than the error of the linear mean-square approximation given by Hall et al. [1]. The final products of the mathematical analysis are explicit formulas which allow the direct determination of all parameters and the maximum error for any desired number n of subdivisions of [1,2].