Some comparison theorems for nonnegative splittings of matrices
In an earlier paper [Lin. Algebra Appl. 154-156, 433-455 (1991; Zbl 0732.65024)], the author gave some theorems on the comparison of asymptotic convergence rates of nonnegative splittings of matrices which extended the result of \textit{V. A. Miller} and \textit{M. Neumann} [Numer. Math. 47, 427-434 (1985; Zbl 0569.65027)]. This paper extends these results and gives theorems concerning two splittings \(A = M_ 1 - N_ 1\), \(A = M_ 2 - N_ 2\) of the square matrix \(A \in \mathbb{C}^{n \times n}\). The splitting is nonnegative if \(M^{-1}N\) is nonnegative. The new results involve the matrices \(A^{-1} M_ 1\), \(M_ 1A^{-1}\), \(A^{- 1} M_ 2\), \(M_ 2 A^{-1}\).
scientific article; zbMATH DE number 569156