On generalized \(H\)-matrices (Q1763825)

The authors discuss the properties of generalized \(M\)-matrices and of generalized \(H\)-matrices and give some new and interesting equivalent conditions for this type of matrices. The generalized \(M\)-matrices and the generalized \(H\)-matrices arise in the numerical solution of 2D or 3D Euler partial differential equations in fluid dynamics and in the study of invariant of dynamical systems. Also, some remarks are made, to improve an incorrect definition of the block generalized positive definite matrix given by \textit{R. Nabben} [see Definition 5.1 in the article ``On a class of matrices which arise in the numerical solution of Euler equations'', Numer. Math. 63, 411--431 (1992; Zbl 0764.65019)].