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Operation Count w/ LU Decomposition
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[QUOTE="brmath, post: 4516074, member: 486151"] You are quite right that the lower left portion of the matrix is mostly zeros and that there are four entries to zero out. Assuming that the diagonal entry is a and the entry right below it to be zeroed out is b, you can multiply the "a" row by b/a and you are ready to subtract. I would count b/a as a single multiplication, but depending on who is looking it could count as a multiplication and a division. You'd better ask about that. If you are not sure, set up the matrix with the first row all 1's, the 2nd all 2's, the 3rd 4's, the 4th 8's and the 5 15's, except where there are zeros. (this choice for the rows is just to make the arithmetic easy). Now go ahead and get rid of those 4 non-zero items. How many multiplications does it really take? How many non-zero entries will you have on the upper triangle? How many multiplications does it take to get rid of each one? [/QUOTE]
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