Inexact inner–outer Golub–Kahan bidiagonalization method: A relaxation strategy

We study an inexact inner–outer generalized Golub–Kahan algorithm for the solution of saddle-point problems with a two-times-two block structure. In each outer iteration, inner system has to be solved which in theory done exactly. Whenever is getting large, exact solver is, however, no longer efficient or even feasible and iterative methods must used. focus this article on numerical showing influence accuracy system. Emphasis further given reducing computational cost, defined as total number iterations. develop relaxation techniques intended dynamically change tolerance iteration minimize illustrate our findings Stokes problem validate them mixed formulation Poisson problem.