Polynomial acceleration of iterative schemes associated with subproper splittings (Q1112548)

After the splitting \(A=B-C\) with N(B)\(\subset N(A)\) the consistent system \(Ax=b\) is solved by the iteration \(Bv_{k+1}=Cv_ k+b\) in a fixed subspace complementary to N(B) and the acceleration \(x_{k+1}=\sum^{k+1}_{i=0}\alpha^ i_{k+1}v_ i\) with \(\sum^{k+1}_{i=0}\alpha^ i_{k+1}=1\). Here A and B are positive semidefinite \(n\times n\) matrices. The proofs use spectral properties of generalized inverses. Seven special cases are worked out.