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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
| ASCII Text | x | ||
| 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. | |||
| BibTex | x | ||
| @article{ 10.1109/T-C.1975.224330, author = {J.B. Kioustelidis and J.K. Petrou}, title = {A Piecewise Linear Approximation of Log2x with Equal Maximum Errors in All Intervals}, journal ={IEEE Transactions on Computers}, volume = {24}, number = {9}, issn = {0018-9340}, year = {1975}, pages = {858-861}, doi = {http://doi.ieeecomputersociety.org/10.1109/T-C.1975.224330}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - A Piecewise Linear Approximation of Log2x with Equal Maximum Errors in All Intervals IS - 9 SN - 0018-9340 SP858 EP861 EPD - 858-861 A1 - J.B. Kioustelidis, A1 - J.K. Petrou, PY - 1975 KW - Approximate computation KW - approximate evaluation of elementary functions KW - binary logarithm KW - linear Chebyshev approximation. VL - 24 JA - IEEE Transactions on Computers ER - | |||
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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