What are the convergence criteria for the Gauss-Seidel method?
An example of an AI chatbot conversation about convergence criteria for the Gauss-Seidel method.
What are the convergence criteria for the Gauss-Seidel method?
The Gauss-Seidel method converges if the matrix is either diagonally dominant or symmetric positive definite.
Can you explain what diagonally dominant means?
A matrix is diagonally dominant if, for each row, the absolute value of the diagonal element is greater than the sum of the absolute values of the other elements in that row.
Are there any exceptions to these criteria?
Yes, there are cases where the method may converge even if the criteria are not strictly met, but these are exceptions and not guaranteed.
How can I check if a matrix is diagonally dominant?
You can check each row of the matrix by comparing the absolute value of the diagonal element to the sum of the absolute values of the other elements in that row.
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