Paper Info
Title
Efficient Approaches for Enclosing the United Solution Set of the Interval Generalized Sylvester Matrix Equation
Abstract
We investigate the interval generalized Sylvester matrix equation AXB+CXD=F. We propose a necessary condition for its solutions, and also a sufficient condition for boundedness of the whole solution set. The main effort is performed to develop techniques for computing outer estimations of the so-called united solution set of this interval system. First, we propose a modified variant of the Krawczyk operator, reducing significantly computational complexity, compared to the 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 A, B, C and D and in both of them we suppose that the midpoints of A and C are simultaneously diagonalizable as well as for the midpoints of the matrices B and D. Numerical experiments are given to illustrate the performance of the proposed methods.
Year
DOI
Venue
2015
10.1016/j.apnum.2017.12.003
Applied Numerical Mathematics
Keywords
Field
DocType
Interval arithmetic,Generalized Sylvester matrix equation,Krawczyk operator,Preconditioning
Discrete mathematics,Combinatorics,Kronecker product,Diagonalizable matrix,Midpoint,Matrix (mathematics),Operator (computer programming),Solution set,Sylvester matrix,Mathematics,Computational complexity theory
Journal
Volume
ISSN
Citations 
126
0168-9274
0
PageRank 
References 
Authors
0.34
9
2
Name
Order
Citations
PageRank
Marzieh Dehghani-Madiseh161.47
Milan Hladík226836.33