α-type Matrices And Pseudo-sp Ectral Localizations

The class of H-matrices is an important class of matrices,and widely use d in Quantum Theory,Cybernetics and Bioengineering.In this thesis,three subcl asses of H-matrices,namely geometrically weighted irreducible α-matrices,alg ebraically weighted α-matrices and algebraically weighted irreducible α-matrice s are introduced and studied.By applying their nonsingularity we also study the corresponding eigenvalue localizations,and pseudospectral localizations by introdu cing algebraically weighted norm,concretely:Firstly,geometrically weighted irreducible α-matrices are introduced based on geometrically weighted α-matrices and the irreducibility of matrices.It is pr oved that geometrically weighted irreducible α-matrices are nonsingular H-mat rices.A new eigenvalue localization set is also obtained.Secondly,we study the algebraically weighted α-matrices and algebraically weighted irreducible α-ma trices.By their nonsingularity two eigenvalue localizations are obtained.Furtherm ore,an algebraically weighting norm is defined,and used to give a new pseudos pectral localization,called algebraically weighted pseudospectral localization.It is proved that the new pseudospectral localization is better than the Gersgorin-type pseudospectral localization,and is better than Brauer-type and CKV-type pseud ospectral localizations in somecase by the numerical examples.