Kalajda, O. F.; Gonta, T. T. Construction of bilateral polynomials of the Lagrange type for multidimensional functions. (Ukrainian) Zbl 0961.41003 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 1997, No. 1, 39-45 (1997). Let \((x_{i},y_{j})\) be points of approximation. For a two-dimensional function \(F(x,y)\) the authors propose bilateral formulas of approximation \(\widehat L_{mn}= \sum_{i=0}^{m}\sum_{j=0}^{n}\widehat\omega_{i}(x) \widehat\psi_{j}(y)\phi(x_{i},y_{j})-C(x+x_{0})^{m+1}/(m+1)!\), \(\widetilde L_{mn}= \sum_{i=1}^{m+1}\sum_{j=1}^{n+1}\widetilde\omega_{i}(x) \widetilde\psi_{j}(y)\phi(x_{i},y_{j})-C(x+x_{0})^{m+1}/(m+1)!\), where \(\widehat\omega_{i}(x)= \prod_{\nu=0,\nu\neq i}^{m}(x-x_{\nu})/(x_{i}-x_{\nu})\), \(\widehat\psi_{j}(y)= \prod_{\mu=0,\mu\neq j}^{n}(y-y_{\mu})/(y_{j}-y_{\mu})\), \(\widetilde\omega_{i}(x)= \prod_{\nu=1,\nu\neq i}^{m+1}(x-x_{\nu})/(x_{i}-x_{\nu})\), \(\widetilde\psi_{j}(y)= \prod_{\mu=1,\mu\neq j}^{n+1}(y-y_{\mu})/(y_{j}-y_{\mu})\). For the functions \(\exp\{xy\}\) and \(\exp\{x+y\}\) some numerical analysis is presented. Reviewer: A.D.Borisenko (Kyïv) MSC: 41A10 Approximation by polynomials Keywords:bilateral polynomials; Lagrange type; multidimensional functions PDFBibTeX XMLCite \textit{O. F. Kalajda} and \textit{T. T. Gonta}, Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 1997, No. 1, 39--45 (1997; Zbl 0961.41003)