Interpolation by L-spline functions of many variables

  • Yu. S. Zav'yalov


The choice of function space allows us to make conclusions in the multidimensional case that are analogous to results in the theory of spline functions of one variable. We establish the minimum norm property, the existence and uniqueness of a solution of the interpolation problem, the property of best approximation, and the convergence of interpolation processes.


Function Space Norm Property Spline Function Minimum Norm Interpolation Problem 
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Literature cited

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    J. Ahlberg, E. Nilson, and J. Walsh, The Theory of Splines and Their Applications, Academic Press, New York (1967).Google Scholar
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    M. H. Schultz and R. S. Varga, “L-splines,” Numer. Math.,10, No. 4, 345–369 (1967).Google Scholar
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    P. M. Prenter, “Piecewise L-splines,” Numer. Math.,18, No. 3, 243–253 (1971).Google Scholar
  4. 4.
    Yu. S. Zav'yalov, “Interpolation by bicubic splines,” Vychislit. Sistemy, No. 38, 74–101 (1970).Google Scholar
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    Yu. S. Zav'yalov, “An extremal property of bicubic splines and a smoothing problem,” Vychislit. Sistemy, No. 42, 109–158 (1970).Google Scholar

Copyright information

© Consultants Bureau 1974

Authors and Affiliations

  • Yu. S. Zav'yalov
    • 1
  1. 1.Mathematics Institute, Siberian BranchAcademy of Sciences of the USSRUSSR

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