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Original Articles

Fitting functions of Jackson type for three-dimensional data

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Pages 157-174 | Received 14 Sep 2017, Accepted 22 Mar 2018, Published online: 09 Apr 2018

References

  • N.I. Achieser, Theory of Approximation, Dover Publications, New York, 1992.
  • M.D. Buhmann, Approximation and interpolation with radial functions in Lp-norm, in Multivariate Approximation and Applications, N. Dyn, D. Leviatan, D. Levin, and A. Pinkus, eds., Cambridge University Press, Cambridge, UK, 2001, pp. 25–43.
  • P. Chandra, Trigonometric approximation of functions in Lp-norm, J. Math. Anal. Appl. 275 (2002), pp. 13–26. doi: 10.1016/S0022-247X(02)00211-1
  • E.W. Cheney, Approximation Theory, AMS Chelsea Publishing, Providence (RI), 1982.
  • P.J. Davis, Interpolation and Approximation, 2nd ed., Dover Publications, New York, 1976.
  • D. Jackson, On the degree of convergence of the development of a continuous function according to Legendre polynomials, Trans. Am. Math. Soc. 13 (1912), pp. 305–318.
  • D. Jackson, On approximation by trigonometric sums and polynomials, Trans. Am. Math. Soc. 13 (1912), pp. 491–515. doi: 10.1090/S0002-9947-1912-1500930-2
  • D. Jackson, On the accuracy of trigonometric interpolation, Trans. Am. Math. Soc. 14 (1913), pp. 453–461. doi: 10.1090/S0002-9947-1913-1500957-1
  • D. Jackson, Theory of Approximation, Vol. 11, American Mathematical Society Colloquium Publications, New York, 1930.
  • D. Jackson, Problems of closest approximation on a two-dimensional region, Amer. J. Math. 60 (1938), pp. 436–446. doi: 10.2307/2371305
  • D. Jackson, Fourier Series and Orthogonal Polynomials, Carus Mathematical Monographs, Vol. 6, Mathematical Association of America, Oberlin, OH, 1941.
  • L. Leindler, Trigonometric approximation in Lp-norm, J. Math. Anal. Appl. 302 (2005), pp. 129–136. doi: 10.1016/j.jmaa.2004.07.049
  • G.G. Lorentz, Approximation of Functions, AMS Chelsea Publishing, Providence (RI), 1986.
  • V.N. Mishra, Some problems of approximation of functions in Banach spaces, Ph.D. Thesis, Indian Institute of Technology, Roorkee.
  • V.N. Mishra and L.N. Mishra, Trigonometric approximation of signals (functions) in Lp(p≥1)-norm, Int. J. Contemp. Math. Sci. 7(19) (2012), pp. 909–918.
  • L.N. Mishra, V.N. Mishra, K. Khatri, and Deepmala, On the trigonometric approximation of signals belonging to generalized weigthed Lipschitz W(Lr,ξ(t))(r≥1)-class by matrix (C1.Np) operator of conjugate series of its Fourier series, App. Math. Comput. 237 (2014), pp. 252–263. doi: 10.1016/j.amc.2014.03.085
  • R. Schaback and H. Wendland, Characterization and construction of radial basis functions, in Multivariate Approximation and Applications, N. Dyn, D. Leviatan, D. Levin, and A. Pinkus, eds., Cambridge University Press, Cambridge, UK, 2001, pp. 1–24.
  • D. Shepard, A two-dimensional interpolation for irregularly spaced data, in Proceedings of the 1968 ACM National Conference, New York, 1968, pp. 517–524.

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