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3 cards from this section. Quick, good the night before a test.
What is a primary reason for using stopping criteria in numerical methods?
Think about wasting time on iterations.
State one stopping criterion related to the function value.
The function value must be close to zero.
What does the criterion |f(xₙ)| < 𝜖 signify in numerical methods?
Think about the definition of a root.
True or False: The maximum number of iterations is a valid stopping criterion.
Consider what would happen without a limit.
You are solving an equation using the Newton-Raphson method. Your current approximation xₙ = 3.5, the next approximation xₙ₊₁ comes out to be 3.100. Analyze whether to stop based on |xₙ - xₙ₋₁| < 𝜖 if 𝜖 = 0.1.
Check the difference carefully.
Consider using stopping criteria. You set a maximum of 50 iterations for an equation where each iteration feels like it gives you closer answers. However, after 49 iterations, the change between answers is becoming minimal, what would you do?
Weigh the trade-off between efficiency and accuracy.
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