EFFICIENT CHEBYSHEV ECONOMIZATION FOR ELEMENTARY FUNCTIONS

Yıl 2019, Cilt: 61 Sayı: 1, 33 - 56, 30.06.2019

Esmat Bekır

https://doi.org/10.33769/aupse.459815

Öz

This paper presents economized power series for trigonometric and hyperbolic

functions. It determines the smallest range over which a function need to be computed

and scales the Chebyshev polynomials accordingly. Thus reduced degree polynomials

(and hence reduced computations) can be obtained while maintaining the same

accuracy as those unscaled higher degree polynomials.

Anahtar Kelimeler

Chebyshev polynomial, economization, trigonometric functions

Kaynakça

• 1. C. Lanczos, Tables of Chebyshev polynomials, Applied Math. Series, U.S. Bur. Stand. 9, Washington, Government Printing Office, 1952.
• 2. J.C. Mason and D.C. Handscomb, Chebyshev Polynomials, Chapman &Hill/CRC, Boca Raton, FA, 2003.
• 3. J. Rivlin, Chebyshev Polynomials, John Wiley &Sons Inc., New York, NY, 1990.
• 4. B.W. Arden and K.N. Astill, Numerical Algorithms: Origins and Applications, Addison-Wesley, Reading, MA, 1970.
• 5. M.A. Snyder, Chebyshev Methods in Numerical Approximation, Prentice Hall, Englewood Cliffs, NJ, 1966.
• 6. L. Fox and I.B. Parker, Chebyshev Polynomials in Numerical Analysis, Oxford University Press, London, 1968.
• 7. C.W. Clenshaw, “A Note on the Summation of Chebyshev Series” http://www.ams.org/journals/mcom/1955-09-051/S0025-5718-1955-0071856-0/S0025-5718-1955-0071856-0.pdf
• 8. Ying Guang Shi, Power Orthogonal Polynomials, Nova Science Publishers, New York, NY, 2006.
• 9. M. Abramowitz and I.A. Stegun (Ed.), Handbook of Mathematical Functions, Dover Publications, Inc., New York, N.Y., 1970.
• 10. G.P. Michon, Numericana.com, http://home.att.net/~numericana/