Assignment 3
Marking Scheme and TA Comments
Question 1:
Most students did very well on question 1.
Some mistakes:
- Didn't use permutation matrix at all, either in the LU factorization or
computing Pb (-2 marks)
- Errors in matrix multiplication (including use of permutation matrix)
(-1 mark)
- Not considering largest absolute value element when permuting rows for
LU (-1 mark)
- Unnecessary interchanging of rows (-1 mark)
For part (b), as long as the students correctly did forward and back
substitution full marks were awarded (even if LU with pivoting from part
(a) was incorrect).
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Question 2:
The following is the marking scheme for Q2:
(a) 3 marks for correctly setting up the matrix A,
1 mark for setting up vector b, and
1 mark for correct value for f_hat
(b) 3 marks for correct error bound formula,
2 marks for correct matlab code
(I took off 1 mark if there is any inconsistency in the norm used or
incorrect calculation)
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Question 3:
I divided the 10 marks as follows:
4 marks for the code,
2 marks for formatted, reasonable results,
2 marks for discussion of condition number v.s. n, and
2 marks for discussion of correct digits v.s. condition number.
1. The students did quite well in the code part.
2. Some students didn't format the results well. I usually took 1 mark off.
3. Some students failed to answer the two requested sub-questions. They
lost 2 marks for each.
4. Some students didn't get appropriate, reasonable and quantitative
relationships for condition number v.s. n and correct digits v.s.
condition number. I deducted 1 or 2 points depending on the quality
of the answer.