The Schur Complement Property Of Nekrasov Matrix And Application

The Nekrasov matrix is a matrix of special nature in the class of H matrices,which has been widely used in many fields.Due to the particularity of its own structure,it has attracted the attention of many experts and scholars.In this article we discussed the Nekrasov matrix of Schur for arbitrary submatrix.On this basis,the Schur line of diagonal matrix Nekrasov estimate of we made.Further application based on Schur fill related iterative method to deal with the problem solving system of linear equations.In chapter one,This paper mainly introduces the application background,research status and recent work of Nekrasov matrix,and gives the basic symbols and related definitions.In chapter two,On the basis of the particularity of the element of Nekrasov matrix and the correlation of Schur complement,the condition of whether Schur complement or Nekrasov matrix is given.Furthermore,the closure of the Schur complement of the Nekrasov matrix and the mathematical induction method are used to estimate the diagonally dominant degree of the Schur complement of the Nekrasov matrix about its arbitrary submatrix,and the existing conclusions are extended and improved.In chapter three,Using the results of the second chapter first gained Nekrasov Schur fill the inverse matrix of the matrix spectral radius estimates,we further applied to the matrix of coefficient matrix is Nekrasov in the large-scale system of linear e-quations.Based on the Schur complement relevant iteration method,design the both can reduced order processing and has good convergence of the iterative algorithm is presented.The advantages of its conclusion is verified by examples.