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Which of the following has a problem in convergence for a system with long radial lines?
- a)Newton-Raphson
- b)Gauss-Seidel
- c)Both Newton-Raphson and Gauss Siedel
- d)None of the two methods
Correct answer is option 'B'. Can you explain this answer?
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Explanation:
Gauss-Seidel Method:
The Gauss-Seidel method is an iterative technique used to solve a system of linear equations. In this method, the system is solved one variable at a time, using the most recent values of the other variables.
When dealing with systems that have long radial lines, the Gauss-Seidel method can encounter convergence issues. This is because the method relies on the values of neighboring variables to update the current variable. In systems with long radial lines, the influence of neighboring variables may not propagate quickly enough, leading to slow convergence or even divergence.
Therefore, the Gauss-Seidel method may have problems with convergence for systems with long radial lines.
Newton-Raphson Method:
The Newton-Raphson method is a root-finding algorithm that can also be used to solve systems of nonlinear equations. This method involves linearizing the system of equations and iteratively updating the solution until convergence is achieved.
Unlike the Gauss-Seidel method, the Newton-Raphson method does not rely on neighboring variables for updating a particular variable. Instead, it uses the Jacobian matrix to calculate the direction and magnitude of the update. Therefore, the Newton-Raphson method is not as sensitive to the spatial arrangement of variables in the system.
In conclusion, the Gauss-Seidel method is more likely to encounter convergence issues for systems with long radial lines compared to the Newton-Raphson method.
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Which of the following has a problem in convergence for a system with long radial lines?a)Newton-Raphsonb)Gauss-Seidelc)Both Newton-Raphson and Gauss Siedeld)None of the two methodsCorrect answer is option 'B'. Can you explain this answer?
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