Gasca, Mariano; Pena, Juan Manuel Interpolation, elimination and totally positive matrices. (Spanish) Zbl 0792.41004 Rev. R. Acad. Cienc. Exactas Fís. Nat. Madr. 86, No. 2, 175-194 (1992). The present paper deals with Neville elimination strategy. Such a method has important advantages in comparing with the usual strategy of Gauss when the matrices fulfill properties as that to be totally positive. The authors show the connection between polynomial interpolation formulae and matricial elimination techniques. The Aitken-Neville interpolation formula is specially considered in order to elucidate the corresponding Neville elimination strategy. The last section of this paper is devoted to explain some applications of total positivity in computer aided design. Reviewer: J.Illán González (La Habana) MSC: 41A05 Interpolation in approximation theory 65D05 Numerical interpolation 65F05 Direct numerical methods for linear systems and matrix inversion 65D17 Computer-aided design (modeling of curves and surfaces) Keywords:Neville elimination strategy; matricial elimination techniques; Aitken- Neville interpolation formula; total positivity; computer aided design PDFBibTeX XMLCite \textit{M. Gasca} and \textit{J. M. Pena}, Rev. R. Acad. Cienc. Exactas Fís. Nat. Madr. 86, No. 2, 175--194 (1992; Zbl 0792.41004) Full Text: EuDML