Convergence of Generalized SOR, Jacobi and Gauss–Seidel Methods for Linear Systems

In this paper, we study the convergence of generalized Jacobi and generalized Gauss–Seidel methods for solving linear systems with symmetric positive definite matrix, L-matrix and H-matrix as co-efficient matrix. A generalization of successive overrelaxation (SOR) method for solving linear systems is proposed and convergence of the proposed method is presented for linear systems with strictly diagonally dominant matrices, symmetric positive definite matrices, M-matrices, L-matrices and for H-matrices. Finally, numerical experiments are carried out to establish the advantages of generalized SOR method over generalized Jacobi, generalized Gauss–Seidel, and SOR methods. © 2020, Springer Nature India Private Limited.