Issue No.09 - September (1975 vol.24)
J.B. Kioustelidis , Research Center for National Defense
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. . 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].
Approximate computation, approximate evaluation of elementary functions, binary logarithm, linear Chebyshev approximation.
J.B. Kioustelidis, J.K. Petrou, "A Piecewise Linear Approximation of Log2x with Equal Maximum Errors in All Intervals", IEEE Transactions on Computers, vol.24, no. 9, pp. 858-861, September 1975, doi:10.1109/T-C.1975.224330