Representation of functions in control systems
Heading:
| 1Popov, BO 1Karpenko Physico-Mechanical Institute of the National Academy of Science of Ukraine, Lviv, Ukraine |
| Kosm. nauka tehnol. 1998, 4 ;(4):151–155 |
| https://doi.org/10.15407/knit1998.04.151 |
| Publication Language: Ukrainian |
Abstract: We propose a hardly efficient approach for calculating mathematical functions in space control systems. The approach is based on a balanced approximation of the functions by rational Chebyshev splines. Expressions are obtained for the errors and link borders for the main mathematical functions.
|
| Keywords: space control systems |
References:
1. Nemeth G. Relative rational approximation of function exp(x), Math. Notes, 21 (4), 581-586 (1977) [In Russian].
https://doi.org/10.1007/BF01787660
https://doi.org/10.1007/BF01787660
2. Popov B. A. Uniform Approximation by Splines, 272 p. (Naukova Dumka, Kiev, 1989) [in Russian].
3. Popov B. A., Tesler G. S. Computation of functions on electronic computers: handbook, 600 p. (Nauka Dumka, Kiev, 1984) [In Russian].
4. Braess D. On the conjecture of Meinardus on rational approximation to exp(x). J. Approxim. Theory, 40 (4), 375-379 (1984).
https://doi.org/10.1016/0021-9045(84)90012-1
https://doi.org/10.1016/0021-9045(84)90012-1
5. Computer approximation, Eds J. F. Hart, E. V. Cheney et al., 334 p. (Wiley, New York, 1968).
6. Kalautari B., Kalantari J. High order iterative methods for approximation square roots. BIT, 36 (2) 395-396 (1996).
https://doi.org/10.1007/BF01731991
https://doi.org/10.1007/BF01731991
7. Meinardus G. Approximation of functions. Theory and numerical methods, 198 p. (Springer, Berlin, 1967).
https://doi.org/10.1007/978-3-642-85643-3
https://doi.org/10.1007/978-3-642-85643-3
8. Schulte M. J., Omar J., Swartzlander E. E. Optimal initial approximations for the Newton-Rephson division algorithm. Computing, 53 (3-4), 233-242 (1994).
https://doi.org/10.1007/BF02307376