Generation In The Numerical Solution Of Euler Equations Of The Generalized H-matrix And Matrix Spectral Estimation Study

This thesis presents a systematic research on some types of special matricessuch as generalized positive definition matrices, generalized H-matrices andnonnegative irreducible matrices. The thesis consists three parts with fivechapters.In part one (chapter two), we give some new properties of generalizedpositive definition matrices, and two determinant inequalities about generalizedpositive definition matrices are presented.The second part (chapter three) contributes to generalized H-matrices.Based on the relationships between generalized M-matrices and generalizedH-matrices with M-matrices and positive definition matrices, we obtain severalequivalent conditions for generalized H-matrices, some remarks on two resultsin [R. Nabben, on a class of matrices which arise in the numerical solution ofEuler equations, Numer. Math. 1992, 63: 411-431] are given.In the last part (chapter four and five), for the Perron root of nonnegativeirreducible matrices, a new sequence of upper bounds is presented, whichconvergence is discussed. The comparison of the new sequence with the knownones is supplemented with two numerical examples. Finally, by the properties ofnonnegative matrices, we give some inequalities about the largest singularvalues and spectral radius of matrices.