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• To see that this loop performs the same computation, lets work out its dependence structure.
• First label each iteration with the element of A to which it assigns:

  

• The loop body is

   A[k  ,k  -k  ] := A[k  -1,k  -k  ]+A[k  ,k  -k  -1]
  
  

• E.g. iteration does:

   A[2,1] := A[1,1]+A[2,0]