The Effect of The new Preconditioned Iterative Techniques on The Speed and Efficiency of Convergence of The Successive Over Relaxation (SOR ) Method
DOI:
https://doi.org/10.65405/asdwx074Keywords:
Iterative Techniques - Iterative matrix - spectral radius - Successive Over Relaxation(SOR)method - Eigen value - Preconditioned - convergenceAbstract
In some scientific fields and numerical analysis, there are problems whose solution requires knowledge of certain numerical methods for linear systems. Direct methods can be used to solve such systems easily. However, when the coefficient matrices are large and complex, traditional direct methods become slow, often lead to complicated solutions, and require a long time to reach the final solution. This work proposes modern Iterative methods for solving Linear systems to achieve a fast and convergent solution. Among these methods, we briefly covered Jacobi and Gauss – Seidel methods, then studied the Successive Over Relaxation (SOR) method. We obtained new Iterative Techniques to reach a fast Solution for The linear System. Through discussion and analysis, we arrived at two types of Preconditioned Iterative techniques, where new Preconditioned Iteration matrices were developed for the Successive Over Relaxation method. When testing the spectral radius of these matrices, they gave fast and convergent Solutions. We compared them to see which was faster. The analytical results showed that both were faster than the traditional Successive Over Relaxation(SOR)method.
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