Bojanov, Borislav D.Dimitrov, Dimitar K. [UNESP]2014-05-272014-05-272001-04-01Mathematics of Computation, v. 70, n. 234, p. 671-683, 2001.0025-5718http://hdl.handle.net/11449/66486The purpose of this paper is to show certain links between univariate interpolation by algebraic polynomials and the representation of polyharmonic functions. This allows us to construct cubature formulae for multivariate functions having highest order of precision with respect to the class of polyharmonic functions. We obtain a Gauss type cubature formula that uses ℳ values of linear functional (integrals over hyperspheres) and is exact for all 2ℳ-harmonic functions, and consequently, for all algebraic polynomials of n variables of degree 4ℳ - 1.671-683engExtended cubature formulaGaussian extended cubature formulaPolyharmonic functionPolyharmonic order of precisionArtigo10.1090/S0025-5718-00-01206-0WOS:000167738400013Acesso aberto2-s2.0-0035531380