J.A.Kalinovsky, Y.E.Boyarinova
Èlektron. model. 2018, 38(2):83-92
https://doi.org/10.15407/emodel.38.02.083
ABSTRACT
The results of computation experiment have been presented on reducing the amount of computations using representations of hypercomplex nonlinearities, such as exponential curve, trigonometric and hyperbolic functions, as compared to their direct calculation.
KEYWORDS
hypercomplex number system, the exponential function, trigonometric function, hyperbolic function, the amount of computation.
REFERENCES
1. Sinkov, M.V., Boyarinova, J.E. and Kalinovsky, J.A. (2010), Konechnomernye giperkompleksnye chislovye sistemy. Osnovy teorii. Primeneniya. [Finite-dimensional hypercomplex number systems. Fundamentals of the theory. Applications], IPRI, Kyiv, Ukraine.
2. Kalinovsky, J.A. (2007), “Development of methods of HNS theory for mathematical modeling and computer calculations”, Dr Sci. (Tech.) dissertation, Institute for Information Recording of NAS of Ukraine, Êyiv, Ukraine.
3. Hamilton, W.R. (1848), “Researches respecting quaternions: First series”, Transactions of the Royal Irish Academy, Vol. 21, part1, pp.199-296.
4. Kähler, U. (1998), “Die Anwendung der hyperkomplexen Funktionentheorie auf die Losung partieller Differentialgleichungen”, available at: www.tu-chemnitz.de /mathematik/prom_habil/promint.pdf
5. Brackx, F. (1979), “The exponential function of a quaternion variable”, Applicable Analysis, Vol. 8, pp. 265-276.
https://doi.org/10.1080/00036817908839234
6. Scheicher, K., Tichy, R.F. and Tomantschger, K.W. (1997), “Elementary Inequalities in hypercomplex numbers”, Anzeiger, Vol. II, no. 134, pp. 3-10.
7. Holin, H. “The quaternionic exponential and beyond”, available at: http://www.bigfoot.com/~Hubert.Holin.
8. Eberly, D. (1999), “Quaternion algebra and calculus”, available at: http://www.magic-software.com
9. Klingener, F. (2001), “Summary of dual and quaternion mathematics for kinematics”, available at: www.BrockEng.com/VMech /Quaternions/ kinemath.pdf.
10. Ude, A. “Filtering in a unit quaternion space for model-based object tracking”, available at: www.cns.atr.jp/~aude/publications/ras99.pdf
11. Liefke, H. (1998), “Quaternion calculus for modeling rotations in 3D space”, available at: www.liefke.com/hartmut
12. Olariu, S. (2000), “Complex numbers in three dimensions”, available at: arXiv: math. CV/0008119 v1 (accessed Aug. 16, 2000).
13. Olariu, S. (2000), “Commutative complex numbers in four dimensions”, available at: arXiv: math. CV/0008119 v1 (accessed August 16, 2000).
14. Sinkov, M.V., Boyarinova, J.E., Kalinovsky, J.A., Postnikova, T.G. and Sinkova, T.V. (2005), “Algorithm-software tools for analytical computations over hypercomplex numbers in computer mathematical system MAPLE”, Data Recording, Storage and Processing, Vol. 7, no. 2, pp. 18-24.