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Cardinal Hermite interpolation using positive definite functions

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Abstract

In this paper, we study cardinal Hermite interpolation by using positive definite functions. Among other things, we establish a procedure that employs the multiquadrics for cardinal Hermite interpolation.

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References

  1. M. Abramowitz and I.A. Stegun,Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series 55 (Dover, 1966).

  2. C. de Boor, K. Höllig and S.D. Riemenschneider, Fundamental solutions for multivariate difference equations, Amer. J. Math. 111 (1989) 403–415.

    Google Scholar 

  3. M. Chang, Polyharmonic cardinal Hermite spline interpolations, Ph.D. Dissertation, The University of Connecticut (1991).

  4. K. Guo and X. Sun, Scattered data interpolation by linear combinations of translates of conditionally positive definite functions, Numer. Funct. Anal. Optim. 12 (1991) 137–152.

    Google Scholar 

  5. R.L. Hardy, Multiquadratic equations of topography and other irregular surfaces, J. Geophys. Rep. 76 (1971) 1905–1915.

    Google Scholar 

  6. Y. Katznelson,Harmonic Analysis (Dover, New York, 1976).

    Google Scholar 

  7. S.L. Lee, Fourier transform of B-splines and fundamental splines for cardinal Hermite interpolations. Proc. Amer. Math. Soc. 57 (1976) 291–296.

    Google Scholar 

  8. P.R. Lipow and I.J. Schoenberg, Cardinal interpolation and spline functions III: Cardinal Hermite interpolation, J. Lin. Alg. Appl. 6 (1973) 273–304.

    Google Scholar 

  9. W. Madych and S. Nelson, Polyharmonic cardinal splines, J. Approx. Theory 60 (1990) 141–156.

    Google Scholar 

  10. W. Madych and S. Nelson, Polyharmonic cardinal splines: a minimization property, J. Approx. Theory 63 (1990) 303–320.

    Google Scholar 

  11. M.J. Marsden and S.D. Riemenschneider, Cardinal Hermite interpolation: convergence as the degree tends to infinity. Trans. Amer. Math. Soc. 235 (1978) 221–224.

    Google Scholar 

  12. S.D. Riemenschneider, Multivariate cardinal interpolation, in:Approximation Theory VI Vol. 2, eds. C.K. Chui, L.L. Schumaker and J.D. Ward (Academic Press, 1989) pp. 561–580.

  13. S.D. Riemenschneider and K. Scherer, Cardinal Hermite interpolation with box splines, Constr. Approx. 3 (1987) 223–238.

    Google Scholar 

  14. S.D. Riemenschneider and K. Scherer, Cardinal Hermite interpolation with box splines II, Numer. Math. 58 (1991) 591–602.

    Google Scholar 

  15. E.M. Stein and G. Weiss,Introduction to Fourier Analysis on Euclidean Spaces (Princeton University Press, 1971).

  16. G.M. Watson,A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge University Press, 1962).

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Authors and Affiliations

  1. Department of Mathematics, Southwest Missouri State University, 65804, Springfield, MO, USA

    Xingping Sun

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  1. Xingping Sun
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Communicated by C. Brezinski

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Xingping Sun Cardinal Hermite interpolation using positive definite functions. Numer Algor 7, 253–268 (1994). https://doi.org/10.1007/BF02140686

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  • DOI: https://doi.org/10.1007/BF02140686

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