Improved Generalized Classical Iterative Technique for Solving Linear System
DOI:
https://doi.org/10.63075/z16qyn32Keywords:
System of Linear Equations, Generalized Gauss–Jacobi (GGJ), Generalized Gauss–Seidel (GGS), Composite Refinement of Jacobi–Gauss–Seidel (CRJGS), Composite Refinement of Gauss–Seidel–Jacobi (CRGSJ).Abstract
One of the major problems of linear algebra is to find the solution of a system of linear equations (SOLEs). Among iterative techniques, one of the most important topics of interest is SOLEs. This type of systems can be found in a wide range of disciplines, such as natural and social sciences, engineering, medicine, and business. Iterative methods are typically used to solve sparse SOLEs. A better method- Improved Generalized Classical Iterative Techniques (IGCT) has been put forward in this study. This procedure can be used when the coefficient matrix is diagonally dominant (SDD), irreducibly diagonally dominant (IDD), an M-matrix, symmetric positive definite under some specifications or an H-matrix. Such systems can frequently be an outcome of ordinary differential equations (ODEs) and partial differential equations (PDEs). The suggested approach has a good spectral radius and convergence rate and fewer iterations. Its action has been confirmed by numerical experiments, such as comparison to classical methods on a number of nonlinear problems of literature. The execution was done with the help of MATLAB (R2014b), a high-level computational programming language.
