In the common trigonometric regression model we investigate the optimal design problem for the estimation of the individual coeecients, where the explanatory variable varies in the interval ?a; a]; 0 < a : It is demonstrated that the structure of the optimal design depends sensitively on the size of the design space. For many cases optimal designs can be found explicitly, where the complexity o...

Numerical algorithms for D-optimum design usually rely on a discretization of the design space into a finite set X. Their speed then depends on the cardinality of this set. We show in this paper how it is possible, during the search for an optimum design, to remove from X some design points that cannot be support points of the optimum design, and therefore to accelerate the algorithms.

For the heat equation on a bounded subdomain Ω of R, we investigate the optimal shape and location of the observation domain in observability inequalities. A new decomposition of L(R) into heat packets allows us to remove the randomization procedure and assumptions on the geometry of Ω in previous works. The explicit nature of the heat packets gives new information about the observability const...

Article history: Received 14 August 2009 Received in revised form 9 December 2009 Accepted 18 December 2009 Available online 21 January 2010