Abstract
In this paper, we estimate the following quantity sep [ ( A , B ) , ( C , D ) ] = min ‖ X ‖ F = 1 ‖ A X D − B X C ‖ F , where A , B ∈ C m × m , C , D ∈ C n × n and ‖ ⋅ ‖ F is the Frobenius norm. In terms of the generalized Schur decomposition and Weiestrass canonical form of the regular matrix pair, lower and upper bounds of sep [ ( A , B ) , ( C , D ) ] are derived, respectively. The results are illustrated by numerical examples.
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