What is the concept of relaxation methods in Numerical Analysis?

Numerical Analysis Questions



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What is the concept of relaxation methods in Numerical Analysis?

Relaxation methods in Numerical Analysis refer to iterative techniques used to solve systems of equations or find the roots of equations. These methods involve repeatedly updating the approximate solution by considering the current solution and the residual error. The idea is to gradually improve the solution by relaxing the constraints and allowing for small errors in each iteration. This iterative process continues until a desired level of accuracy is achieved. Relaxation methods are commonly used in solving linear systems, such as the Gauss-Seidel method and the Successive Over-Relaxation (SOR) method.