Criteria For Generalized Nekrasov Matrices

The class of generalized Nekrasov matrix is a class of important special ma-trices,which arises in various applications.It plays an important role in numer-ical algebra,mthematical physics,cybernetics theory,electrical system the-ory,mathematics of economics,statistics and so on. Especially in recent years,asan important application generalized Nekrasov matrix attracts more interests inthe study.Many scholars do a lot of work in generalized Nekrasov matrix , butmost of them is related to the nature of the research. At present studies on thepractical criteria for generalized Nekrasov matrix is rare.For any given matrixA = (aij),the Subscript collection n is divided intodi?erent parts, through the usage of properties of the matrix elements,this pa-per gives some practical su?cient conditions for generalized Nekrasov matrix byconstructing special positive diagonal matrices.In chapter one, we introduce the applied background ,the present situationof research on Generalized Nekrasov matrix,we also present the summary of thispaper and several basic symbols,definitions,lemmas as well. In chapter two, thenumber set n is divided into two parts based on the relations of |aii| and Ri(A)through the usage of the properties of the matrix elements . By constructingspecial positive diagonal matrix and using recurrence and inequality techniquesand Mathematical induction, we obtain a class of judging methods for generalizedNekrasov matrix .In chapter three, the number set n is divided into three partsbased on the relations of |aii| and Ri(A),by constructing special positive diagonalmatrices,a practical su?cient criterion for generalized Nekrasov matrix is pro-posed, then we choose a coe?cient factor that is not more than 1, and multiplyit with some elements in N1 or N3. We discuss the relation of |bii| and Ri(B)of matrixAD = (bij) = B with recurrence and inequality techniques to get someother broader su?cient conditions for generalized Nekrasov matrix. In each class,some numerical examples illustrate the e?ectiveness of our results. Finally,theirmutual independence is illustrated by some numerical examples.