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On the characterization of totally positive matrices. (English) Zbl 0758.15014

Approximation theory, spline functions and applications, Proc. NATO Adv. Study Inst., Maratea/Italy 1991, NATO ASI Ser., Ser. C 356, 357-364 (1992).
[For the entire collection see Zbl 0741.00016.]
The present survey shows different ways to obtain characterizations of totally positive (TP) and strictly totally positive (STP) matrices by factorization and by the nonnegativity of some minors.
In authors’ investigations of alternative elimination strategies to Gaussian elimination for matrix factorization. They are led to study the simplest of them, the so called Neville elimination. By means of this simplest elimination strategy the authors prove some new characterizations of TP and STP matrices.

MSC:

15B48 Positive matrices and their generalizations; cones of matrices
15A23 Factorization of matrices
65F05 Direct numerical methods for linear systems and matrix inversion
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