An algebraic multilevel iterative method of incomplete factorization for Stieltjes matrices (Q1571188)

A more general formulation is given to a multilevel iterative method of incomplete factorization that was proposed earlier for solving five-point systems of equations with symmetric positive definite \(M\)-matrices. The quality of a preconditioner is improved with the use of special matrix polynomials, which recursively relate the preconditioners of two adjacent levels. The upper and lower bounds for the degrees of polynomials are determined from the conditions that an optimal order of computational complexity is preserved and an optimal rate of convergence is achieved.