Generalization of the interval TOR method for solving interval linear systems

Iterative methods for solving interval linear systems were presented in this paper. By generalizing interval diagonal matrices to interval band matrices, a generalization of the interval two-parameter overrelaxation method (GITOR) was introduced, and the convergence analysis of the proposed method was discussed. Specifically, if the coefficient matrices of the system are strictly diagonally dominant (SDD) matrices, interval M-matrices, or interval H-matrices, the proposed method converges under any initial approximation. Furthermore, an upper bound on the spectral radius of the iterative matrices was provided for interval strictly diagonally dominant matrices. Finally, numerical examples for each type of mentioned interval matrix were studied, demonstrating the efficiency of the proposed method.