An error bound on the AOR method for solving linear systems

AbstractWe investigate the numerical stability, for the symmetric positive definite and consistently ordered matrix A, of the AOR iterative method to obtain the solution of the linear system Ax = b. We give an error bound ∥εn∥2⩽1D2(ω−1)2+μ2∣ω(r−ω)∣2∥δn∥2−2(ω−1)2〈δn,δn+1〉+2μ2∣ω(r−ω)∣〈∣δn∣,∣δn+1∣〉+∥δn+1∥2 for the error estimation