Practice Successive Over-relaxation (sor) (25.14.3) - Solutions of Linear Systems: Existence, Uniqueness, General Form

Practice: Successive Over-Relaxation (SOR)

Lesson 25.14.3Solutions of Linear Systems: Existence, Uniqueness, General Form

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9 questions

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6 sample questions

Question 1.
Define Successive Over-Relaxation (SOR).
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Think about its relationship to the Gauss-Seidel method.
Question 2.
What is the relaxation parameter ω used for?
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Consider how it affects convergence.
3Question 3.
What does SOR stand for?
- Simple Over-Relaxation
- Successive Over-Relaxation
- Simplicity in Over-Relaxation
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Think about what this method improves upon.
4Question 4.
True or False: The relaxation parameter ω can exceed 1.
- True
- False
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Remember what effect different ω values have.
Question 5.
Given a system of linear equations, derive a SOR iteration formula taking ω = 1.5.
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Work through the Gauss-Seidel method steps first to build your SOR formulation.
Question 6.
Formulate a strategy for determining the best relaxation parameter for a specific system of non-linear equations.
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Use graphical representation to visualize convergence speed with varying ω values.

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