Iterative refinement using splitting methods

AbstractFor every nonsingular matrix A, we show there exists a convergent splitting A = M − N with M = DQ or M = QD where Q and D are unitary and diagonal respectively. Also, if A has an LU decomposition, there exists a convergent splitting A = M − N with triangular M. An example of construction of the desired triangular matrix M is given for p-cyclic matrices. This result allows us to establish some iterative refinement methods for linear systems, which are often better than the usual iterative refinement methods with regard to complexity and storage requirements. The convergence of the refinement process is studied