TP perturbation of TN matrices and totally positive directions

Here, we define and consider (linear) TP-directions and TP-paths for a totally nonnegative matrix, in an effort to more deeply understand perturbation of a TN matrix to a TP matrix. We give circumstances in which a TP-direction exists and an example to show that they do not always exist. A strategy to give (nonlinear) TP-paths is given (and applied to this example). A long term goal is to understand the sparsest TP-perturbation for application to completion problems.

Supported by FEDER Funds through Programa Operacional Factores de Competitividade - COMPETE and by Portuguese Funds through FCT - “Fundação para a Ciência e a Tecnologia”, within the Project PEst-OE/MAT/UI0013/2014.