Solution Methods for R-Linear Problems in Cn

We consider methods, both iterative and direct, for solving an R–linear system Mz +M#z = b in C with a pair of matrices M,M# ∈ Cn×n and a vector b ∈ C. Algorithms that avoid formulating the problem as an equivalent real linear system in R are introduced. Conversely, this implies that real linear systems in R can be solved with the methods proposed in this paper. Our study is motivated by Krylov subspace iterations with which using the real formulation can be disastrous in the standard linear case. Related matrix analysis and spectral theory are developed. AMS subject classifications: 15A04, 65F10