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Interpolation, elimination and totally positive matrices. (Spanish) Zbl 0792.41004

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.

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)
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