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Perfect splines with boundary conditions and their application to certain extremal problems

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Approximation Theory and its Applications

Abstract

In this paper we consider two problems. The first is connected with the optimal recovery of functions satis fyiog boundary conditions. The second is the characterization of the unique function whose r-th derivative has minimum L∞-norm, taking given values of alternating signs and satisfying boundary conditions.

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References

  1. Bojanov, B., σ-Perfect Splines and Their Application to Optimal Recovery Problems, J. Complexity 3(1987), 429–450.

    Article  MATH  MathSciNet  Google Scholar 

  2. Bojanov, B., Characterization of the Smoothest Interpolant, SIAM J. Math. Anal. Appl. 6 (1994), 1642–1655.

    Article  MathSciNet  Google Scholar 

  3. Bojanov, B., Hakopian, H. and Sahakian, A., Spline Functions and Multivariate Interpolations, Kluwer Academic Publishers, 1993.

  4. Dirong, C., Perfect Splines with Boundary Conditions of Least Norm, J. Approx. Theory 77 (1994), 191–201.

    Article  MATH  MathSciNet  Google Scholar 

  5. Karlin, S., Total Positivity, 1, Stanford, California, Stanford University Press, 1968.

    Google Scholar 

  6. Karlin, S., Michelli, C., The Fundamental Theorem of Algebra for Monsplines Satisfying Boundary Condition, Israel J. Math. 11(1972), 405–451.

    Article  MATH  MathSciNet  Google Scholar 

  7. Melkman, A., Interpolation by Splines Satisfying Mixed Boundary Conditions, Israel J. Math. 4 (1974), 369–381.

    Article  MathSciNet  Google Scholar 

  8. Micchelli, C., Rivlin, T. and Winograd, S., The Optimal Recovery of Smooth Functions, Numer. Math. 26(1976), 191–200.

    Article  MATH  MathSciNet  Google Scholar 

  9. Pinkus, A., On Smoothest Interpolants, SIAM J. Math. Anal. 6(1988), 1431–1441.

    Article  MathSciNet  Google Scholar 

  10. Schumaker, L., Spline Functions-Basic Theory, Wiley-Interscience New York, 1981.

    MATH  Google Scholar 

  11. Shvabauer, O., On the Widths of Class of Differentiable Functions, Mat. Zametki, 34 (1983), 663–681.

    MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Veliko Turnovo University, 5000, Veliko Turnovo, Bulgaria

    Chrisina Draganova

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  1. Chrisina Draganova
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Partially supported by Ministry of Science under Project MM-414.

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Draganova, C. Perfect splines with boundary conditions and their application to certain extremal problems. Approx. Theory & its Appl. 14, 44–55 (1998). https://doi.org/10.1007/BF02836928

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  • DOI: https://doi.org/10.1007/BF02836928

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