Research On Sine Schur Complement For Several Special Matrix

In matrix theory, linear control theory and numerical analysis and other disci-plines, often will a special class of matrices some research, when the matrix order is too high, we tend to want to come through reduced order processing, so this time we will focus or any of its sub-matrix has the nature of such a matrix is still the matrix, which Schur complement and diagonal-Schur complement plays an important role and is a very useful tool, and also got some important conclusions. on this basis, the for a special class of matrices Schur complement in-depth research, the main contents are as follows:In Chapter l,we introduce some research background and status on our main contents,definitions and theorems.In Chapter 2,In order to further study and promote Schur complements scope, this paper introduces the triangle-Schur complements (diagonal-Schur complement is a special case of triangle-Schur complement when θ=π/2), and uses the proper-ties of strictly product γ-diagonally dominant matrix that the author obtains the triangle-schur complements of strictly product γ-diagonally dominant matrix are strictly product γ-diagonally dominant matrix.Meanwhile,when A is a strictly prod-uct γ-diagonally dominant matrix, we get the upper bounds for ρ[(A/。A(α)θ)-1] and ρ(Jθ);also get ρ[(A/。A(α)θ)-1]< p[A-1] and p(Jθ)≤ρ(J). In the end of the article the author gives the numerical examlie illustrating the effectiveness of the criteria.In Chapter 3,Because of (AW)/α=(A/α)(W/α) is strictly diagonally dom-inant matrix,and (W/α) also is strictly diagonally dominant matrix,so we can get (A/α) is strictly diagonally dominant matrix.From this formula we can use Schur complements properties of the obtained the matrix itself properties. This chapter is to study a class of matrices with special properties,if its Schur complement is strictly diagonally dominant matrix,then itself is strictly diagonally dominant ma-trix. We get Six kinds of such matrices and gives the numerical examlie illustrating the effectiveness of the criteria.