A matrix S is a solvent of the matrix polynomial M(X) Ao Xm +. + Am if M(S) 0 Technical Report [2].If the Ai are scalar matrices, Ai aI, then (1.1) reduces to (1.2) This problem, has been thoroughly studied (Gantmacher,[4]) and we have such classical results as the Cayley-Hamilton theorem and the Lagrange-Sylvester interpolation theorem.
Abstract. In an earlier paper we developed the algebraic theory of matrix polynomials. Here we introduce two algorithms for computing "dominant" solvents. Global convergence of the algorithms under certain conditions is established.
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