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On the E‐Optimality of Block Designs with Unequal Block Sizes
Author(s) -
Brzeskwiniewicz Henryk
Publication year - 1989
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710310520
Subject(s) - mathematics , block (permutation group theory) , generalization , eigenvalues and eigenvectors , block design , matrix (chemical analysis) , combinatorics , mathematical optimization , mathematical analysis , physics , materials science , quantum mechanics , composite material
In this paper an inequality for the smallest positive eigenvalues of the C ‐matrix of a block design are derived. This inequality is a generalization of a result by Constantine (1982) to the case of unequal block sizes. On the basis of the above result a certain E ‐optimality criterium of block designs is given. Furthermore coefficient e d has been introduced which permits to assess how close the block design is from the optimal one.