EFFICIENT CHEBYSHEV ECONOMIZATION FOR ELEMENTARY FUNCTIONS

Esmat Bekır

doi:10.33769/aupse.459815

Research Article

EFFICIENT CHEBYSHEV ECONOMIZATION FOR ELEMENTARY FUNCTIONS

Year 2019, , 33 - 56, 30.06.2019

Esmat Bekır

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

Abstract

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.

Keywords

Chebyshev polynomial, economization, trigonometric functions

References

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/

Year 2019, , 33 - 56, 30.06.2019

Esmat Bekır

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

Abstract

References

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/

There are 10 citations in total.

Details

Primary Language	English
Subjects	Engineering
Journal Section	Review Articles
Authors	Esmat Bekır 0000-0001-8500-5131
Publication Date	June 30, 2019
Submission Date	September 13, 2018
Acceptance Date	March 22, 2019
Published in Issue	Year 2019

Cite

APA	Bekır, E. (2019). EFFICIENT CHEBYSHEV ECONOMIZATION FOR ELEMENTARY FUNCTIONS. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering, 61(1), 33-56. https://doi.org/10.33769/aupse.459815
AMA	Bekır E. EFFICIENT CHEBYSHEV ECONOMIZATION FOR ELEMENTARY FUNCTIONS. Commun.Fac.Sci.Univ.Ank.Series A2-A3: Phys.Sci. and Eng. June 2019;61(1):33-56. doi:10.33769/aupse.459815
Chicago	Bekır, Esmat. “EFFICIENT CHEBYSHEV ECONOMIZATION FOR ELEMENTARY FUNCTIONS”. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering 61, no. 1 (June 2019): 33-56. https://doi.org/10.33769/aupse.459815.
EndNote	Bekır E (June 1, 2019) EFFICIENT CHEBYSHEV ECONOMIZATION FOR ELEMENTARY FUNCTIONS. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering 61 1 33–56.
IEEE	E. Bekır, “EFFICIENT CHEBYSHEV ECONOMIZATION FOR ELEMENTARY FUNCTIONS”, Commun.Fac.Sci.Univ.Ank.Series A2-A3: Phys.Sci. and Eng., vol. 61, no. 1, pp. 33–56, 2019, doi: 10.33769/aupse.459815.
ISNAD	Bekır, Esmat. “EFFICIENT CHEBYSHEV ECONOMIZATION FOR ELEMENTARY FUNCTIONS”. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering 61/1 (June 2019), 33-56. https://doi.org/10.33769/aupse.459815.
JAMA	Bekır E. EFFICIENT CHEBYSHEV ECONOMIZATION FOR ELEMENTARY FUNCTIONS. Commun.Fac.Sci.Univ.Ank.Series A2-A3: Phys.Sci. and Eng. 2019;61:33–56.
MLA	Bekır, Esmat. “EFFICIENT CHEBYSHEV ECONOMIZATION FOR ELEMENTARY FUNCTIONS”. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering, vol. 61, no. 1, 2019, pp. 33-56, doi:10.33769/aupse.459815.
Vancouver	Bekır E. EFFICIENT CHEBYSHEV ECONOMIZATION FOR ELEMENTARY FUNCTIONS. Commun.Fac.Sci.Univ.Ank.Series A2-A3: Phys.Sci. and Eng. 2019;61(1):33-56.