### The order of the best transfinite interpolation of functions with bounded laplacian with the help of harmonic splines on box partitions

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Mangeron D.I. "Sopra un problema al contorno per un’equatione differentiable alle derivate parziali di quartordine conle caratteristice reali dopie", *Rend. Accad. Sci. Fis. Mat. Napoli*, 1932; 2: pp. 28-40.

Coons S.A. "Surface for computer-aided design of space forms", *Project MAC report MAC-TR-41*, Cambridge, 1967; pp. 3-30.

Birkhoff G., Gordon W.J. "The draftsman’s and related equations", *J. of Approx. Theory*, 1968; 1: pp. 199-208.

Anikeenko A.M., Litvin O.M., Rvachov V.L., Safonov M.O. "On formula of expansion in the neighbourhood of a circle", *Dopovidi AN URSR. Ser. A*, 1972; 2: pp. 99-100. (in Ukrainian)

Gordon W., Hall G. "Construction of curvilinear coordinate systems and application to mesh generation", *International J. for Numerical Methods in Engineering*, 1973; 7: pp. 461-477.

Dyken C., Floater M. "Transfinite mean value interpolation", *Computer Aided Geometric Design*, 2009; 26: pp. 117-134.

Floater M.S. "Mean value coordinates", *Computer Aided Geometric Design*, 2003; 20: pp. 19-27.

Litvin O.M. *Interlination of functions*, Kharkiv, Osnova, 1993. (in Ukrainian)

Bejancu A. "Transfinite Thin Plate Spline Interpolation", *Constructive Approximation*, 2011; 34: pp. 237-256.

Klimenko V.T. "Approximation of functions of two variables by harmonic splines", *Ukrainian Math. J.*, 1995; 47: pp. 1190-1196. (in Russian)

Babenko V.F., Leskevich T.Yu. "Approximation of some classes of multivariable functions by harmonic splines", *Ukrainian Math. J.*, 2012; 64: pp. 1011-1024. (in Russian)

Babenko Yu., Leskevych T. "On the $$$L_p$$$-error of adaptive approximation of bivariate functions by harmonic splines", *Applicable Analysis*, 2014; 93: pp. 171-189.

Kuzmenko D., Skorokhodov D. "Optimization of transfinite interpolation of functions with bounded Laplacian by harmonic splines on box partitions", *J. of Approx. Theory*, 2016; 209: pp. 44-57.

Ahlberg J.H., Nilson E.N. *The Theory of Splines and Their Applications*, New York, Acad. Press, 1967.

Litvin O.M. "Interlination of bivariate functions on $$$M$$$ ($$$M \geqslant 2$$$) lines with the highest algebraic accuracy", *Ukrainian Math. J.*, 1992; 44: pp. 1498-1510. (in Russian)

Litvin O.M., Sergienko I.V. "Methods of function approximation and modern computer technologies", *Cyber. and System Analysis*, 2007; 43: pp. 64-81. (in Russian)

Hoppe V. "Finite elements with harmonic interpolation functions", *Proc. Conf. MAFELAP (J. R. Whiteman, ed.)*, London, Academic Press, 1973; pp. 131-142.

Natterer F., Teubner B.G. *The mathematics of computerized tomography*, Stuttgart, John Wiley and Sons, Ltd., Chichester, 1986; 222 p.

Kounchev O. *Multivariate polysplines: applications to numerical and wavelet analysis*, London, Academic Press, 2001.

Devore R. *Nonlinear approximation*, Cambridge University Press, Acta Numerica, 1998. pp. 51-150.

Plaskota L. *Noisy information and computational complexity*, New York, Cambridge University Press, 1996; 308 p.

DOI: https://dx.doi.org/10.15421/241811

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