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An inverse central ordering of the nodes is proposed for the Newton interpolation formula. This ordering may improve the stability for certain distributions of nodes. For equidistant nodes, an upper bound of the conditioning is provided. This bound is close to the bound of the conditioning in the Lagrange interpolation formula, whose conditioning is the lowest. This ordering is related to a pivoting strategy of a matrix elimination procedure called Neville elimination. The results are illustrated with examples. [ABSTRACT FROM AUTHOR]

This paper analyses the performance of several versions of a block parallel algorithm in order to apply Neville elimination in a distributed memory parallel computer. Neville elimination is a procedure to transform a square matrix A into an upper triangular one. This analysis must take into account the algorithm behaviour as far as execution time, efficiency and scalability are concerned. Special attention has been paid to the study of the scalability of the algorithms trying to establish the relationship existing between the size of the block and the performance obtained in this metric. It is important to emphasize the high efficiency achieved in the studied cases and that the experimental results confirm the theoretical approximation. Therefore, we have obtained a high predicting ability tool of analysis. Finally, we will present the elimination of Neville as an efficient tool in detecting point sources in cosmic microwave background maps. [ABSTRACT FROM AUTHOR]

Solving linear systems is often required in chemical problems. Besides, birth and death processes occur in many chemical phenomena and the matrices associated to these processes are totally positive, that is, all their minors are nonnegative. Neville elimination is an elimination procedure very useful when dealing with these matrices. Convergence and stability of iterative refinement using Neville elimination are analyzed, in particular when the coefficient matrix is totally positive. Other applications to chemistry are commented and numerical experiments are shown. [ABSTRACT FROM AUTHOR]