A NEW METHOD FOR OBTAINING HIGHLY ACCURATE APPROXIMATIONS ...
[Pages:10]27 Aug 2011-Preprint
A NEW METHOD FOR OBTAINING HIGHLY ACCURATE APPROXIMATIONS TO THE ARCTAN FUNCTION
by
Ulrich H.Kurzweg and
Sidey P.Timmins
(Dept. Mechanical and Aerospace (Sabre Systems Inc. Engineering,University of Florida) U.S.Census Bureau)
INTRODUCTION:
Computing the arctangent is needed in many applied fields, for example, measuring distance on the ellipsoid for navigation, calculating phase in digital signal processing and determining angles in computer graphics. Each of these applications requires that the simple definition of the tangent on a right triangle be inverted. However, this is difficult as the arctangent exhibits a highly non-linear relationship with angle. Methods to calculate the arctangent are usually based upon summation of a Taylor series. This summation is inconvenient because the series converges slowly outside of a narrow range (x ................
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