Neville elimination: an efficient algorithm with application to chemistry

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.