The bounds on components of the solution for consistent linear systems (Q817063)

The author considers a consistent linear system (1) \(Ax=b\), where \(A\) is an \(n\times n\) M-matrix, \(b\) is an \(n\)-dimensional vector in range(\(A\)). The study of the solution of the linear system (1) is very important in the Leontief model of input-output analysis and in a finite Markov chain. The author discusses a special M-matrix linear system, when the matrix \(A\) in linear system (1) is a diagonally dominant L-matrix; this matrix class often appears in the input-output model and in the finite Markov chain.