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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

Posted Wednesday, June 15, 2011 4:22 AM Post #649
 

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Indeed very useful for me, Thanks for sharing.

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