On the characterization of almost strictly totally positive matrices |
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Authors: | M Gasca and J M Pe?a |
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Institution: | (1) Departamento de Matemática Aplicada, Universidad de Zaragoza, Spain |
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Abstract: | A nonsingular matrix is called almost strictly totally positive when all its minors are nonnegative and, furthermore, these
minors are strictly positive if and only if their diagonal entries are strictly positive. Almost strictly totally positive
matrices are useful in Approximation Theory and Computer Aided Geometric Design to generate bases of functions with good shape
preserving properties. In this paper we give an algorithmic characterization of these matrices. Moreover, we provide a determinantal
characterization of them in terms of the positivity of a very reduced number of their minors and also in terms of their factorizations.
Both authors were partially supported by the DGICYT Spain Research Grant PB93-0310 |
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