The Breadth-one DD-invariant Polynomial Subspace

We demonstrate the equivalence of two classes of $D$-invariant polynomial subspaces introduced in [8] and [9], i.e., these two classes of subspaces are different representations of the breadth-one $D$-invariant subspace. Moreover, we solve the discrete approximation problem in ideal interpolation for the breadth-one $D$-invariant subspace. Namely, we find the points, such that the limiting space of the evaluation functionals at these points is the functional space induced by the given $D$-invariant subspace, as the evaluation points all coalesce at one point

Hermite Positive Definite Solution of a Class of Matrix Equation

AbstractIn this paper, the Hermite positive definite solutions of the nonlinear matrix equation XS+A*X−tA=Q are discussed. A sufficient condition and two necessary and sufficient conditions for the existence of Hermite positive definite solutions for this equation are derived. The existence of minimal Hermite positive definite solution is also studied here, and an iterative method for obtaining the minimal Hermite positive definite solution is given