The Newton iterative method for computing outer inverses with prescribed range and null space is used in the non-stationary Richardson iterative method to develop an iterative method for solving general restricted linear equations. Starting with any suitably chosen initial iterate, our method generates a sequence of iterates converging to the solution. The necessary and sufficient conditions for the convergence along with the error bounds are established. The applications of the iterative method for solving some special linear equations are also discussed. A number of numerical examples are worked out. They include singular square, rectangular, randomly generated rank deficient matrices, full rank matrices and a set of singular matrices given in Matrix Computation Toolbox (mctoolbox) with the condition numbers ranging from order 1016 to 1050. The mean CPU time (MCT) and the error bounds are the performance measures used. Our results when compared with the results obtained by Chen (1997) leads to substantial improvement in terms of both computational speed and accuracy.
Dr. Shwetabh Srivastava and Gupta, D. K., “An Iterative Method for Solving General Restricted Linear Equations”, Applied Mathematics and Computation, vol. 262, pp. 344 - 353, 2015.