For a symmetric positive semidefinite linear system of equations Qx = b, where x = (x1, . . . , xs) is partitioned into s blocks, with s ≥ 2, we show that each cycle of the classical block symmetric Gauss-Seidel (block sGS) method exactly solves the associated quadratic programming (QP) problem but added with an extra proximal term of the form 12‖x−x ‖T , where T is a symmetric positive semidef...

The paper answers several open questions of the alternating direction method of multipliers (ADMM) and the block coordinate descent (BCD) method that are now wildly used to solve large scale convex optimization problems in many fields. For ADMM, it is still lack of theoretical understanding of the algorithm when the objective function is not separable across the variables. In this paper, we ana...

We present numerical methods for solving systems of linear equations originated from the discretisation of two-dimensional elliptic partial diierential equations. We are interested in diierential equations that describe heterogeneous and anisotropic phenomena. We use a nonoverlapping domain decomposition method for solving the linear systems. We describe new local preconditioners for the interf...