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A note on regularity and positive definiteness of interval matrices

Raena Farhadsefat;  Taher Lotfi;  Jiri Rohn — 2012

Open Mathematics

We present a sufficient regularity condition for interval matrices which generalizes two previously known ones. It is formulated in terms of positive definiteness of a certain point matrix, and can also be used for checking positive definiteness of interval matrices. Comparing it with Beeck’s strong regularity condition, we show by counterexamples that none of the two conditions is more general than the other one.

On the local convergence of Kung-Traub's two-point method and its dynamics

Parandoosh Ataei Delshad;  Taher Lotfi — 2020

Applications of Mathematics

In this paper, the local convergence analysis of the family of Kung-Traub's two-point method and the convergence ball for this family are obtained and the dynamical behavior on quadratic and cubic polynomials of the resulting family is studied. We use complex dynamic tools to analyze their stability and show that the region of stable members of this family is vast. Numerical examples are also presented in this study. This method is compared with several widely used solution methods by solving test...

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