3. Which of the following is an iterative method?O Factorization © Gauss Seidel © Gauss Elimination © None of the previous

Break Down the Problem

1. Identify which methods are typically classified as iterative.
2. Understand the purpose of each method listed in the options.

Relevant Concepts

1. Factorization: This generally refers to methods like LU decomposition, which are direct methods rather than iterative.
2. Gauss Seidel: This is an iterative method used to solve linear systems of equations.
3. Gauss Elimination: This is a direct method used to solve linear systems.
4. None of the previous: This indicates that none of the listed methods are iterative.

Analysis and Detail

1. Gauss Seidel is designed to iteratively approach a solution; it refines estimates of the unknowns in the system by using the previous estimates.
2. Both Factorization and Gauss Elimination solve for the exact solution in a finite number of steps and do not involve iteration.

Verify and Summarize

From this analysis, we conclude that the only iterative method listed is the Gauss Seidel method. The other methods are direct techniques and do not involve iteration.

Final Answer

The iterative method among the options provided is Gauss Seidel.