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EFFICIENT CHEBYSHEV ECONOMIZATION FOR ELEMENTARY FUNCTIONS

Year 2019, Volume: 61 Issue: 1, 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, Volume: 61 Issue: 1, 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 Volume: 61 Issue: 1

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.
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