In the framework of inverse linear problems on infinite-dimensional Hilbert space, we prove convergence conjugate gradient iterates to an exact solution problem in most general case where self-adjoint, non-negative operator is unbounded and with minimal, technically unavoidable assumptions initial guess iterative algorithm. The proved always hold space norm (error convergence), as well at other...

The Stokes problem plays an important role in computational fluid dynamics since it is encountered in the time discretization of (incompressible) Navier-Stokes equations by operator-splitting methods [2, 3]. Space discretization of the Stokes problem leads to large scale ill-conditioned systems. The Uzawa (preconditioned) conjugate gradient method is an efficient method for solving the Stokes p...