Schur Complements Of Some Classes Of Structured Matrices And Its Related Problems

The Schur complement as one of the most important topics in matrix theory is applied widely in Control theory,Computational mathematics and Statistics.We in this thesis mainly study the Schur complements of some classes of structured matrices called DZ-type matrices,?-diagonally and product ?-diagonally dominant matrices,concretely,for the Schur complement of DZ-type matrices,we give two sufficient conditions such that the Schur complement of DZ-type matrices is also a DZ-type matrix,and some estimations for the DZ-type diagonally dominant degree.A numerical example is given to show that Schur-based Gauss-Seidel iteration method and conjugate gradient method solve faster the linear system with the coefficient matrix being DZ-type matrices.For the parametered inclusion sets based on the Schur complements of ?-diagonally and product ?-diagonally dominant matrices in [Liu JZ,Huang ZJ.The Schur complements of ?-diagonally and product ?-diagonally dominant matrix and their disc separation,Linear Algebra and its Applications,2010,432:1090-1104],we give its equivalent forms without a parameter,which are all computable.