علیرضا عطایی

In this thesis, first we present the recurrence formulas for computing the approximate inverse factors of tridiagonal matrices using bordering technique. Resulting algorithms are used to approximate the inverse of pivot blocks needed for constructing block ILU preconditioners for solving the block tridiagonal linear systems. Then two new block ILU preconditions for block tridiagonal M-matrices and H-matrices are proposed. Some the theoretical properties for the preconditioners are studied and how to construct preconditioners effectively is also discussed. In next step acquired algorithms(FAIT(1) algorithm and 1.3 algorithm)is applied for GMRES and Bi-CGSTAB methods as perconditioner and it's studied in comparison with two algorithms with number of required iterations for convergence.