2,426 research outputs found
Efficient Approaches for Enclosing the United Solution Set of the Interval Generalized Sylvester Matrix Equation
In this work, we investigate the interval generalized Sylvester matrix
equation and develop some
techniques for obtaining outer estimations for the so-called united solution
set of this interval system. First, we propose a modified variant of the
Krawczyk operator which causes reducing computational complexity to cubic,
compared to Kronecker product form. We then propose an iterative technique for
enclosing the solution set. These approaches are based on spectral
decompositions of the midpoints of , , and
and in both of them we suppose that the midpoints of and
are simultaneously diagonalizable as well as for the midpoints of
the matrices and . Some numerical experiments are given to
illustrate the performance of the proposed methods
Solvability and uniqueness criteria for generalized Sylvester-type equations
We provide necessary and sufficient conditions for the generalized
-Sylvester matrix equation, , to have exactly one
solution for any right-hand side E. These conditions are given for arbitrary
coefficient matrices (either square or rectangular) and generalize
existing results for the same equation with square coefficients. We also review
the known results regarding the existence and uniqueness of solution for
generalized Sylvester and -Sylvester equations.Comment: This new version corrects some inaccuracies in corollaries 7 and
- …