A projection method for semidefinite linear systems and its applications Original Research Article

We study the solution of consistent, semidefinite and symmetric linear systems by iterative techniques. Given a finite sequence of subspaces a block-iterative projection type algorithm is considered. For two specific choices of iteration parameters we show convergence. We apply our results to over and under determined linear equations. These methods are based on decomposing the system matrix into blocks of rows or blocks of columns. Thereby several algorithms, many used in image reconstruction, are presented in a unified way.