Diagonal transformation methods for computing the maximal eigenvalue and eigenvector of a nonnegative irreducible matrix (Q753420)

A diagonal transformation method for computing the maximal eigenvalue and associated eigenvector of a nonnegative irreducible matrix is a sequence of the form \((1)\quad A^{(k+1)}=(S^{(k)})^{-1}A^{(k)}S^{(k)},\) where \(S^{(k)}\) are positive definite diagonal matrices. This paper presents sufficient conditions on \(S^{(k)}\), in a general setting, in which (1) gives a convergent method. These results are then used to study known methods and to construct new ones.