Why would chol fail?

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SingHua Tsai
SingHua Tsai 2018-8-25
评论： SingHua Tsai 2018-8-26
I have a positive definite sparse array Ainv. When I do the chol like
L=chol(Ainv);
M = L*L';
isequal(M,Ainv)
I find that M is not equal to Ainv. How can I use chol to get a right answer?

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Stephan
Stephan 2018-8-25
编辑：Stephan 2018-8-25
Hi,
L*L'
is not the same as
L'*L
The way you do use chol will fulfill the second equation.
You can test with this little example:
A = [7 3; 3 7]
ev = eig(A)
Ch = chol(A)
B1 = Ch'*Ch
B2 = Ch * Ch'
EDIT:
Is Ainv symmetric? If it is, consider that we are dealing with double precision numbers and the operations you perform have rounding errors. See this example:
A = [7 3; 3 7]
Ch = chol(A)
B1 = Ch' * Ch
same = isequal(A,B1)
diff = A-B1
B2 = round(Ch' * Ch)
same2 = isequal(A,B2)
diff2 = A-B2
So there is not a problem with chol, since this is a normal behavior.
Best regards
Stephan

更多回答（1 个）

SingHua Tsai
SingHua Tsai 2018-8-25
Hi,Stephan, thank you for your help and advice. I already revise it as follow
L=chol(Ainv);
M = L'*L;
isequal(M,Ainv)
But M is still not equal to Ainv. I have no idea how to modify it.
Thank for your time.

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