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RE: Flawed LU Calculator

Properan — Wed, 15 Jun 2011 04:22:02 GMT

Indeed very useful for me, Thanks for sharing.

RE: Flawed LU Calculator

Trifon — Thu, 19 Feb 2009 11:24:25 GMT

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.

Flawed LU Calculator

LUsuggestion — Thu, 19 Feb 2009 09:55:15 GMT

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!