Development of Generalized Refinement Strategies in Composite Stationary Iterative Solvers for Linear Systems

Abstract

Linear equations have many applications in natural sciences, engineering, business, social sciences, and medicine. However, solving these types of systems is an important challenge in Numerical Linear Algebra (NLA). There are two types of Methods to solve the systems: direct approaches and indirect approaches.  Iterative methods are very successful in solving large, sparse linear problems.  Iterative approaches often outperform direct methods, particularly when working with sparse coefficient matrices.

This research introduces the composite stationary iterative approach for solving linear systems of equations (GCST). And validate by comparing the proposed method with existing methods, in terms of spectral radius, no. of iterations, and convergence rate. Under specific conditions, proposed methods efficiently solve linear systems with coefficient matrices that are irreducibly diagonally dominant (IDD), strictly diagonally dominant (SDD), M-matrices, or symmetric positive definite. MATLAB (R2014b) was used to compute numerical tests.