Generalized and novel iterative scheme for best approximate solution of large and sparse augmented linear systems.

This article presents a generalized novel iterative technique for obtaining the approximate solution of systems of linear equations Parameters involved in the scheme play a vital role to obtain the rapid and best approximate solution. The technique is applied to some important problems and the results are presented in detail. The article compares the effectiveness of the new presented iterative scheme with modified SOR-like method, generalized SOR and SOR-like method for solving large systems of linear equations. The convergence criteria for the iterative scheme are also analysed and it can be observed in the article that the theoretical derivation is supported by numerical calculations and graphical exhibition. Overall, the article provides a new and effective method with a detailed analysis of its performance and convergence criteria for solving systems of linear equations of the form presented. The newly derived technique has potential applications in various fields of science and engineering where systems of linear equations arise and need to be solved.