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Flawed LU Calculator Expand / Collapse
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Posted Thursday, February 19, 2009 9:55 AM Post #525
 

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Hello. I believe that the way your calculator parses input is giving a flawed result for LU decomposition. Tell me if I'm wrong, but I believe that LU decompositions are only possible on matrices that use only Type III elementary operations. Here is an example, I typed in:

A =

2 1 1
6 4 5
4 1 3

I believe your calculator parses that input and optimizes it to:

6 4 5
4 1 3
2 1 1

I believe this will cause a flawed result because you performed a Type I elementary operation by changing the rows. The U that your calculator returned was:

6.000 4.000 5.000 <---- Type I operation
0.000 -1.667 -0.333
0.000 0.000 -0.600

I did it by hand by only using Type III elementary operations and I got U to be:

2 1 1
0 1 2
0 0 3

I may be wrong, but if I'm correct, I hope this helps. Nice work altogether though!
Posted Thursday, February 19, 2009 11:24 AM Post #526
 

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Thanks for posting here.

For numerical stability reasons, our implementation of LU decomposition uses pivoting. Therefore the original matrix equals to

A= P x L x U

where P is a permatation Matrix. You may try verifying the results (increase the number of decimals) using matrix multiplication and you will get the original matrix.

Trifon Triantafillidis

Lead Developer

Bluebit Software

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