In this thesis, a new iterative method named as the Two-Step Jacobi-Type Iterative Method is introduced and convergence properties of this method are discussed.
This new method is compared with the other two well-known methods which are Jacobi and Gauss-Seidel iterative methods. In order to make comparisons of
convergence properties of Jacobi, Gauss-Seidel and The Two-Step Jacobi-Type Iterative Methods, Fortran program codes for these three methods are written
separately and these programs are run for several systems to obtain numerical results and also to check convergence rates of each method. All this work showed
that the Two-Step Jacobi-Type Iterative Method has better convergence properties compared with the other two well-known methods.

Keywords : Iterative method, convergence, spectral radius