Abstract
The main purpose of this paper is to treat an unsolved problem discussed by S.K. Mitra (1977) concerning the solution of matrix equations which occur in the MINQUE theory of estimating covariance components in a covariance components model of C.R. Rao (1972). Canonical representation of a singular pencil given by Gantmacher (1959) and a theorem of Kucera (1974) were used by S.K. Mitra (1977) to treat the matrix equation AXB+CXD = E. The method used by Mitra (1977) does not extend to the case where the left-hand side of the equation above has one or more additional terms of the same form as AXB and CXD. Necessary and sufficient conditions are established for more general matrix equations whose coefficient matrices are multiparameter matrices along with an algorithm which involves parallel processing to obtain solutions of such matrix equations.
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