AN ELIMINATION METHOD FOR SOLVING MATRIX EQUATIONS

Matrix equations often arise in chemical engineering mathematics (e.g. , the Liapunov and Riccati equations) and it is important to have effi cient methods for their solution. In this paper a new ''elimination'' method is proposed. The method uses the Cayley - Hamilton theorem to o btain relationships between a solution X to a matrix equation, the mat rix coefficients in the equation and the characteristic coefficients o f X. Given initial estimates of the characteristic coefficients it is then possible to formulate an iterative scheme to determine X itself. The method can be used more directly when the matrix equation reduces to finding the m(th) roots of a matrix Q, say, in which case interesti ng algebraic expressions linking the characteristic coefficients of Q and those of its roots can be obtained. Some illustrative examples are given and an attempt is made to compare the new approach with current ly available alternatives.