Computation of ex with the use of large tables
Abstract
A procedure is given for computaion of ex using tables of coefficient of the economized approximating polynomical over a range of positive and negative x. A related procedure that uses continued fractions is also discussed.
The exponential functions was selected to test effectiveness of table lookup methods in the computation of elementary functions. The number of multiplications or divisions required of standard methods is compared with the number required when table lookup is employed.
References
[1]
C. Lanczos, Applied Analysis, Prentice Hall, Inc., Englewood Cliffs, New Jersey, 438-468 (1956).
[2]
"Tables of Chebyshev polynomials Sn(x) and Cn(x)," Applied Mathematics Series, No. 9, National Bureau of Standards (December 1952).
[3]
K. Spielberg, "The representation of power-series in terms of polynomials, rational approximations, and continued fractions," Journal of the Association for Computing Machinery 8, 613-627 (1961).
[4]
E. G. Kogbetliantz, "Computation of eN for - ∞ < N < + ∞∞ using an electronic computer," IBM Journal of Research and Development 1, 2, 110-115 (April 1957).
[5]
D. Cantor, G. Estrin, and R. Turn, "Logarithmic and exponential function evalution in a variable structure computer," IRE Transactions on Electronic Computers EC 11, 155-164 (April 1962).
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IBM Corp.
United States
Publication History
Published: 01 June 1966
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