Numerical solution of the R-linear Beltrami equation

The R-linear Beltrami equation appears in applications, such as in the inverse problem of recovering the electrical conductivity distribution in the plane. In this paper, a new way to discretize the R-linear Beltrami equation is considered. This gives rise to large and dense R-linear systems of equations with structure. For their iterative solution, norm minimizing Krylov subspace methods are devised. In the numerical experiments, these improvements combined are shown to lead to speed-ups of almost two orders of magnitude in the electrical conductivity problem.