Practice Summary Of Key Concepts (1.5) - Introduction to Numerical Methods

Practice: Summary of Key Concepts

Lesson 1.5Introduction to Numerical Methods

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8 questions

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2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define absolute error.
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Think about what values you compare to find the difference.
Question 2.
What does relative error measure?
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Recall how absolute error is expressed in relation to the exact value.
3Question 3.
What is absolute error?
- A. Difference between computed value and exact value
- B. Difference between two approximate values
- C. Error in algorithm design
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Focus on how the term 'absolute' relates to the nature of the error.
4Question 4.
True or False: A well-conditioned problem is one where small changes in input lead to large changes in output.
- True
- False
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Think about the sensitivity in relation to small input changes.
Question 5.
Given an exact solution of 15.7 and a computed solution of 15.3, calculate both absolute and relative errors. Discuss their significance in a practical context.
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Apply your formulas and interpret your results in terms of real-world applications.
Question 6.
Discuss a scenario in which an algorithm may become unstable when solving an ill-conditioned problem. What steps can be taken to secure stability?
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Think critically about how instability can arise and possible remedies.

4 more questions in this section. Enroll free to practise them all.