• GTH-like algorithm
• interval arithmetic
• M-matrix
• non-negative matrix
• triplet representation

The GTH-algorithm is used to solve linear systems where the coefficient matrix is an M-matrices. The GTH-like algorithm is similar to the Gaussian elimination, but it involves only non-negative quantities and no subtractions of quantities of the same sign. The computed solution of the system will have small entry-wise relative error. This work is concerned with an implementation of the GTH-algorithm in interval arithmetic. The goal is describing the solution set of the system when we allow the input data of the algorithm to be interval quantities. We review the existing techniques from the literature. We show some pitfalls in the implementation and we attain some theoretical results that give us more insight about the solution set of the interval system, in particular we give a characterization of the matrices to be used to obtain the extremal values of the interval solution.