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18.3.1. Zero-Stability (for Multistep Methods)
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Mixed questions from across the chapter. Your answers get marked.
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3 cards from this lesson. Good the night before a test.
Try these first
- 1.
What is zero-stability?
Hint
Think about how errors affect numerical solutions.
- 2.
Why is the characteristic equation important?
Hint
Consider what the roots indicate for stability.
- 3.
What is zero-stability?
Hint
Focus on the relationship between errors and solution accuracy.
- 4.
True or False: For zero-stability, roots of the characteristic equation can lie outside the unit circle.
- True
- False
Hint
Think about how this affects solution growth.
- 5.
Given the characteristic polynomial z^3 - 1 = 0, assess the zero-stability of the corresponding method.
Hint
Graph the roots on the complex plane to visualize their location.
- 6.
Consider the characteristic equation z^3 - 2z^2 + z - 1 = 0. Are these roots zero-stable? Provide your reasoning.
Hint
Use the quadratic formula if necessary and evaluate each solution.
Exercises
Total Questions
2
Estimated Time
4 min
Passing Score
70%
Instructions
- Read each question carefully
- You can use hints if you need help
- Complete all questions before submitting
4 more questions available
Enrol freeQuiz
Total Questions
2
Estimated Time
4 min
Passing Score
70%
Instructions
- Read each question carefully
- You can use hints if you need help
- Complete all questions before submitting
1 more question available
Enrol freeChallenge Problems
Total Questions
2
Estimated Time
4 min
Passing Score
70%
Instructions
- Read each question carefully
- You can use hints if you need help
- Complete all questions before submitting