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Bounds for a class of linear functionals with applications to Hermite interpolation

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Abstract

A general estimation theorem is given for a class of linear functionals on Sobolev spaces. The functionals considered are those which annihilate certain classes of polynomials. An interpolation scheme of Hermite type is defined inN-dimensions and the accuracy in approximation is bounded by means of the above mentioned theorem. In one and two dimensions our schemes reduce to the usual ones, however our estimates in two dimensions are new in that they involve only the pure partial derivatives.

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Bibliography

  1. Agmon, S.: Lectures on elliptic boundary value problems. Van Nostrand 1965

  2. Ahlin, A. C.: A bivariate generalization of Hermite's interpolation formula. Math. Comp.18, 264–273 (1964).

    Google Scholar 

  3. Birkhoff, G., Schultz, M., Varga,R.: Piecewise Hermite interpolation in one and two variables with applications to partial differential equations. Num. Math.11, 232–256 (1968).

    Google Scholar 

  4. Bramble, J. H., Hilbert, S. R.: Estimation of linear functionals on Sobolev spaces with applications to Fourier transforms and spline interpolation. S.I.A.M. Num. anal.7, 112–124 (1970).

    Google Scholar 

  5. Morrey, C.: Multiple integrals in the calculus of variations. Berlin-Heidelberg-New York: Springer 1966.

    Google Scholar 

  6. Smith, K. T.: Inequalities for formally positive integro-differential forms. Bull. A.M.S.67, 368–370 (1961).

    Google Scholar 

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Authors and Affiliations

  1. Dep. of Mathematics White Hall, Cornell University, 14850, Ithaca, N.Y., USA

    J. H. Bramble

  2. Dep. of Mathematics, Ithaca College, 14850, Ithaca, N.Y., USA

    S. R. Hilbert

Authors
  1. J. H. Bramble
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  2. S. R. Hilbert
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Additional information

This research was supported in part by the National Science Foundation under grant number N.S.F.-G.P.-9467.

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Bramble, J.H., Hilbert, S.R. Bounds for a class of linear functionals with applications to Hermite interpolation. Numer. Math. 16, 362–369 (1971). https://doi.org/10.1007/BF02165007

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  • DOI: https://doi.org/10.1007/BF02165007

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