- #1
WCMU101
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Hey all. I've written an algorithm to find the Cholesky decomposition of a symmetric, positive-definite matrix (A). I've used the algorithm from: http://en.wikipedia.org/wiki/Cholesky_decomposition#Avoiding_taking_square_roots
Ok here is my question. My current algorithm solves for A = LDLT, however I would also like to solve for A = LTDL. I've seen the results of both decompositions and it looks like they are related. From what I've seen it looks like the L returned from L'DL is just L from cholesky inverted about the positively sloped diagonal. And same for the D. So for example:
A =
4 2 2
2 4 2
2 2 4
A = LDL'
L =
1 0 0
0.5 1 0
0.5 0.333333 1
D =
4 0 0
0 3 0
0 0 2.66667
A = L'DL
L =
1.0000 0 0
0.3333 1.0000 0
0.5000 0.5000 1.0000
D =
2.6667 0 0
0 3.0000 0
0 0 4.0000
So my question. How can I relate the L from LDL' decomp with the L from L'DL decomp (mathematically).
Thanks,
Nick.
Ok here is my question. My current algorithm solves for A = LDLT, however I would also like to solve for A = LTDL. I've seen the results of both decompositions and it looks like they are related. From what I've seen it looks like the L returned from L'DL is just L from cholesky inverted about the positively sloped diagonal. And same for the D. So for example:
A =
4 2 2
2 4 2
2 2 4
A = LDL'
L =
1 0 0
0.5 1 0
0.5 0.333333 1
D =
4 0 0
0 3 0
0 0 2.66667
A = L'DL
L =
1.0000 0 0
0.3333 1.0000 0
0.5000 0.5000 1.0000
D =
2.6667 0 0
0 3.0000 0
0 0 4.0000
So my question. How can I relate the L from LDL' decomp with the L from L'DL decomp (mathematically).
Thanks,
Nick.