Practice Stopping Criteria - 5.1.5 | 5. Solution of Algebraic and Transcendental Equations | Mathematics - iii (Differential Calculus) - Vol 4
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5.1.5 - Stopping Criteria

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is a primary reason for using stopping criteria in numerical methods?

💡 Hint: Think about wasting time on iterations.

Question 2

Easy

State one stopping criterion related to the function value.

💡 Hint: The function value must be close to zero.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What does the criterion |f(xₙ)| < 𝜖 signify in numerical methods?

  • The function has a solution
  • The function value is near zero
  • There are no solutions

💡 Hint: Think about the definition of a root.

Question 2

True or False: The maximum number of iterations is a valid stopping criterion.

  • True
  • False

💡 Hint: Consider what would happen without a limit.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

💡 Hint: Check the difference carefully.

Question 2

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?

💡 Hint: Weigh the trade-off between efficiency and accuracy.

Challenge and get performance evaluation