An alternative method for SPP with full rank (2,1)-block matrix and nonzero right-hand side vector

Abstract

We propose an alternative method to solve large linear saddle point problems arising from computational sciences and engineering such as finite element approximations to Stokes problems, image reconstructions, tomography, genetics, statistics, and model order reductions for dynamical systems. Such problems have large sparse 2-by-2 block structure coefficient matrices with zero (2,2)-block matrix. A new technique is presented to solve saddle point problems with full row rank (2,1)-block matrix and nonzero right-hand side vector. By constructing a projection matrix and transforming the original problem into a least squares problem, a new reduced least squares problem is solved via the well-known iterative method LSMR. Numerical experiments show that this new method works very well for the specified saddle point systems.