Title :
Tight bounds for the trace of a matrix product
Author :
Lasserre, Jean B.
Author_Institution :
Lab. d´´Autom. et d´´Anal. des Syst., CNRS, Toulouse, France
fDate :
4/1/1997 12:00:00 AM
Abstract :
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
Keywords :
matrix algebra; lower bounds; matrix product trace; monotonic convergence; scalar parameter; symmetric matrix; tight bounds; upper bounds; Difference equations; Differential equations; Filtering; Kalman filters; Maximum likelihood detection; Nonlinear filters; Null space; Riccati equations; Silicon compounds; Wiener filter;
Journal_Title :
Automatic Control, IEEE Transactions on
