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A Piecewise Linear Approximation of Log2x with Equal Maximum Errors in All Intervals
September 1975 (vol. 24 no. 9)
pp. 858-861
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. [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].
Index Terms:
Approximate computation, approximate evaluation of elementary functions, binary logarithm, linear Chebyshev approximation.
Citation:
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, Sept. 1975, doi:10.1109/T-C.1975.224330
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