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Tight bounds for the trace of a matrix product

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1 Author(s)
Lasserre, J.B. ; Lab. d''Autom. et d''Anal. des Syst., CNRS, Toulouse, France

We propose a family of new upper and lower bounds for the trace of the matrix product AB when A, or B is symmetric. Those bounds depend on a scalar parameter, and both converge monotonically to tr(AB) when this parameter vanishes, thus providing arbitrary close approximations. Even large values of the parameter yield very good bounds

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Automatic Control, IEEE Transactions on  (Volume:42 ,  Issue: 4 )