Block SOR methods for rank-deficient least-squares problems

Accelerated SOR-like method for augmented linear systems

“…The above assumptions are necessary to ensure the existence of a unique solution in the above augmented linear system (1.1). The augmented linear system (1.1) arises in many different applications of scientific computing such as weighted least-squares problems [18,22,27], finite element discretization of the Navier-Stokes equations [13][14][15], constrained optimization [25], equilibrium system and saddle point problems [7,19], etc.…”

On semi-convergence of the Uzawa–HSS method for singular saddle-point problems

“…This kind of system of linear equations arises in a variety of scientific and engineering applications, such as computational fluid dynamics, constrained optimization, optimal control, weighted least-squares problems, electronic networks, computer graphic etc; see [1][2][3][4] and the references therein. In addition, we can also obtain saddle-point linear systems from the mixed or hybrid finite element discretization of secondorder elliptic problems [5] or the meshfree discretization of some partial differential equations [6,7].…”

On semi-convergence of a class of relaxation methods for singular saddle point problems

“…This kind of system of linear equations arises in a variety of scientific and engineering applications, such as computational fluid dynamics, constrained optimization, optimal control, weighted least-squares problems, electronic networks, computer graphic, the constrained least squares problems and generalized least squares problems etc; see [2,9,18,23,28,29] and the references therein. In addition, we can also obtain saddle point linear systems from the meshfree discretization of some partial differential equations [12,20] or the mixed hybrid finite element discretization of second order elliptic problems [11].…”