Fariborzi Araghi, M., Froozanfar, F. (2015). A method to obtain the best uniform polynomial approximation for the family of rational function. Iranian Journal of Optimization, 7(1), 753-766.
M. A. Fariborzi Araghi; F. Froozanfar. "A method to obtain the best uniform polynomial approximation for the family of rational function". Iranian Journal of Optimization, 7, 1, 2015, 753-766.
Fariborzi Araghi, M., Froozanfar, F. (2015). 'A method to obtain the best uniform polynomial approximation for the family of rational function', Iranian Journal of Optimization, 7(1), pp. 753-766.
Fariborzi Araghi, M., Froozanfar, F. A method to obtain the best uniform polynomial approximation for the family of rational function. Iranian Journal of Optimization, 2015; 7(1): 753-766.
A method to obtain the best uniform polynomial approximation for the family of rational function
1Department of Mathematics, Islamic Azad university, Central Tehran branch
2Ms.student of Mathematics, Islamic Azad university, Kermanshah branch, Kermanshah, Iran
Receive Date: 20 September 2014,
Revise Date: 20 November 2014,
Accept Date: 20 November 2014
Abstract
In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4ac L 0 and b2-4ac G 0.
[1] Achieser N. I., Theory of Approximation, Ungar, New York, 1956.
[2] Achieser N.I., Theory of Approximation, Dover, New York, translated from Russian, 1992.
[3] Bernstein S.N., Extremal Properties of Polynomials and the Best Approximation of Continuous Functions of Single Real Variable, State United Scientific and Technical Publishing House, translated from Russian, 1937.
[4] Cheney E.W., Introduction to Approximation Theory, Chelsea, New York, 1982.
[5] Dehghan M., Eslahchi M.R., Best uniform polynomial approximation of some rational functions,Computers and Mathematics with applications, 2009.
[6] Eslahchi M.R., Dehghan M., The best uniform polynomial approximation to class of the form, Nonlinear Anal., TMA 71 (740_750), 2009.
[7] Golomb M., Lectures on theory of approximation, Argonne National Laboratory, Chicago, 1962.
[8] Jokar S., Mehri B., The best approximation of some rational functions in uniformnorm, Appl. Numer. Math. 55 (204-214), 2005.
[9] Lam B., Elliott D., Explicit results for the best uniform rational approximation to certain continuous functions, J. Approximation Theory 11 (126-133), 1974.
[10] Lorentz G.G., Approximation of Functions, Holt, Rinehart and Winston, New York, 1986.
[11] Lubinsky D. S., Best approximation and interpolation of and itstransforms, J. Approx. Theory 125 (106-115), 2003.
[12] Mason J. C., Handscomb D. C., Chebyshev polynomials, Chapman & Hall/CRC, 2003.
[13]-Newman D.J., Rivlin T. J., Approximation of monomials by lower degree polynomials, Aeq. Math. 14 (451-455), 1976.
[14] Ollin H. Z., Best polynomial approximation to certain rational functions, J.Approx. Theory 26 (389-392), 1979.
[15] Rivlin T. J., An introduction to the approximation of functions, Dover, New York, 1981.
[16] Rivlin T. J., Chebyshev Polynomials. New York: Wiley, 1990.
[17]-Rivlin T. J., Polynomials of best uniform approximation to certain rational functions, Numer. Math. 4 (345-349), 1962.
[18] Timan A.F., Theory of Approximation of a Real Variable, Macmillan, New York, translated from Russian, 1963.
[19] Watson G. A., Approximation Theory and Numerical Methods Chicago, John Wiley & Sons, 1980.
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