Three Types Of Generalized Diagonally Dominant Characteristic Values ​​of Matrix Inversion

Strictly diagonally dominant matrix play an important role in numerical alge-bra、control theory、electric system、economic mathematics and elastic dynamics and so on.As is known,we always need to estimate the infinity or spectral radius for the inverse of matrix both in throry and practical work.For example,the convergence of some interative methods and estimation of some numerical charicteristic and so on.Under the hard work of scholars abroad and home,there are many important fruits. Chapter3and4in this papper solve the estimation for the infinity (or spectral radius) of the inverse of two kind diagonally dominant matrix which have not been done,and then the mumerical example illustrates the effectiveness of the criteria.Given a matrix family,it’s always intersting to know whether some importent properties or structres of the family of the matrices are inherited by their sub-matrices or by the matrices associated with the original matrices.It is known that the schur-complements of strictly diagonally dominant matrix and strictly doubly diagonally dominant matrix are still strictly diagonally dominant matrix and strict-ly doubly diagonally dominant matrix.similar results hold for diagonal-schur com-plements. Triangle-schur complements are introduced in chapter5(diagonal-schur complements is a special case of triangle-schur complement) and we prove that the triangle-schur complements of strictly diagonally dominant matrix and strictly dou-bly diagonally dominant matrix are still strictly diagonally dominant matrix and strictly double diagonally dominant matrix.At the same time,when A is a strictle diagonally dominant matrix,we get||A/。A(α)θ-1||∞≤||A-1||∞.