Assignment 4

                        Marking Scheme and TA Comments


Question 1:

The marking scheme is the following:

(a) they need to specify the choice of the particular vector x.

(b) 3 marks for correctly calculating the matrix multiplication

(c) 1 mark for showing A1 symmetric, either by directly checking 
    A1^T = A1 or by showing A1_ij = A1_ji. 1 mark for showing the 
    second property of the definition of SPD holds

(d) 1 mark for showing n-1 divisions for the multipliers, 2 marks for
    using symmetry to reduce calculations and 2 marks for verifying 
    number of adds and multiplications needed for A1

(e) 3 marks for identifying correct expression for L


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Question 2:

1.  If students didn't output the test results, I took off 1 mark for each 
    subquestion ( 3 points in total if they omitted all the outputs).

2.  A few students misunderstood part (b) and tried to find the permutation 
    matrix P instead of vector p. Also, in part (c), their function works
    with the permutation matrix P instead of vector p. In this case,
    I took off 3 points for part (b) and 2 points for part (c).



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Question 3:

Most students did well. I gave 1 point for parts (1)-(3) and 2 for (4).

For part (a), not discussing the order of convergence (linear/quadratic) 
resulted in a 1 point deduction. Arithmetic errors in taking/evaluating 
the derivative resulted in points lost for that sub-question.

For part (b), Common errors are not discussing the error ratio (-2 
points) or not discussing the rate of convergence (-1 point). If there 
was no table at all but the program is otherwise correct, 3 points were 
deducted.


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Question 4:

Most students did well here also. Common errors include:

- precision issues (-1 point). Points were taken off if the formatting 
  was to 4 decimal places only, because it's impossible to tell if the  
  if behaving as it should.
  No points were taken off if the formatting was in exponential notation.

- not printing to the specified number of iterations: 1 point deducted

- arithmetic errors: 1 point deducted.



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Question 5:

   I wrote the comments on the paper for each student.


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Question 6:

   I marked it based on the strength of argument / coherence of the 
   proof.

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