E-Optimality for Regression Designs of Supplementary Experiments

For the regression model whose linear functional of unknown parameters is estimable, the existence of an E-optimal design for supplementary experiments on the set of all design matrices whose Euclid norm does not exceed a given constant is obtained. The E-optimal designs for supplementary experiments are found in some reasonable regions by spectral decomposition of a matrix. Also, the relationship between the E-optimal design for supplementary experiments and the E-optimal design is obtained. A simple numerical example is given to illustrate the procedure for finding the E-optimal design matrices of supplementary experi - ments.