An error bound for the MAOR method

Suppose Aχ = b is a system of linear equations where the matrix A is symmetric positive definite and consistently ordered. A bound for the norm of the errors k = χ − χk of the MAOR method in terms of the norms of δk = χk − χk−1 and δk+1 = χk+1 − χk and their inner product is derived, εk 22≥1/ω2{((w1 − 1)(w2 − 1) + w1(γ − w2)μ2/2)2 δk 1/2 − 2(w1 − 1) δk,δk+1 + 2w1(ω − w2)μ1/2 δk 2 + δk+1 2 + δk+1 2/2}