Subdirect Sums Of Irreducible Diagonally Dominant And Weakly Chained Diagonally Dominant Matrix

Since Fallot and Johnson proposed the concept of k-subdiect sums of square matrices in 1999,some progress have been made.This important problem is attracting increasing interest due to its important applications in domain decomposition and Schward iteration method of Markov chain.Therefore,the research on the subdiect sums of special matrices is an interesting topic.In this thesis,we try to research the subdiect sums of irreducible diagonally dominant matrices and weakly chained diagonally dominant matrices.First,we provide some numerical examples to show that the subdiect sum of irreducible diagonally dominant matrices is not necessarily an irreducible diagonally dominant matrix,hence,some sufficient conditions are searched to ensure that the subdirect sum of two irreducible diagonally dominant matrices is an irreducible diagonally dominant matrix.Then,we provide some numerical examples to show that the subdiect sums of weakly chained diagonally dominant matrices is not necessarily an weakly chained diagonally dominant matrices too,and some sufficient conditions are also given to ensure that the subdirect sum of two weakly chained diagonally dominant matrices is an weakly chained diagonally dominant matrix.