Cholesky decomposition of normalized matrix
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I need to compute the Cholesky decomposition $A=LL^T$ in order to obtain the matrix $L$.
My matrix $A$ is often badly conditioned (non-positive definite). I am now trying an approach where I normalize $A$ with a matrix $N$ before performing the decomposition. I want to reapply $N$ to the obtained result in order to find the correct matrix $L$.
Is such a method possible, and if so, how and why would it work? Are there any alternative ways to deal with non-positive definite matrices in a Cholesky decomposition?
matrix-decomposition positive-definite
asked Sep 3 at 7:50
Michiel
1
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up vote
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I need to compute the Cholesky decomposition $A=LL^T$ in order to obtain the matrix $L$.
My matrix $A$ is often badly conditioned (non-positive definite). I am now trying an approach where I normalize $A$ with a matrix $N$ before performing the decomposition. I want to reapply $N$ to the obtained result in order to find the correct matrix $L$.
Is such a method possible, and if so, how and why would it work? Are there any alternative ways to deal with non-positive definite matrices in a Cholesky decomposition?
matrix-decomposition positive-definite
asked Sep 3 at 7:50
Michiel
1
If the non psd-ness stems only from numerical imprecision, you could simply stop the Cholesky process when the square root of a very slightly negative number occurs. At that point you have an approximate partial, low rank decomposition, which might be good enough for your purposes.
– kimchi lover
Sep 3 at 13:03
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I need to compute the Cholesky decomposition $A=LL^T$ in order to obtain the matrix $L$.
My matrix $A$ is often badly conditioned (non-positive definite). I am now trying an approach where I normalize $A$ with a matrix $N$ before performing the decomposition. I want to reapply $N$ to the obtained result in order to find the correct matrix $L$.
Is such a method possible, and if so, how and why would it work? Are there any alternative ways to deal with non-positive definite matrices in a Cholesky decomposition?
matrix-decomposition positive-definite
asked Sep 3 at 7:50
Michiel
1
I need to compute the Cholesky decomposition $A=LL^T$ in order to obtain the matrix $L$.
My matrix $A$ is often badly conditioned (non-positive definite). I am now trying an approach where I normalize $A$ with a matrix $N$ before performing the decomposition. I want to reapply $N$ to the obtained result in order to find the correct matrix $L$.
Is such a method possible, and if so, how and why would it work? Are there any alternative ways to deal with non-positive definite matrices in a Cholesky decomposition?
matrix-decomposition positive-definite
matrix-decomposition positive-definite
asked Sep 3 at 7:50
Michiel
1
asked Sep 3 at 7:50
Michiel
1
asked Sep 3 at 7:50
Michiel
1
asked Sep 3 at 7:50
Michiel
1
asked Sep 3 at 7:50
Michiel
1
1
If the non psd-ness stems only from numerical imprecision, you could simply stop the Cholesky process when the square root of a very slightly negative number occurs. At that point you have an approximate partial, low rank decomposition, which might be good enough for your purposes.
– kimchi lover
Sep 3 at 13:03
add a comment |Â
If the non psd-ness stems only from numerical imprecision, you could simply stop the Cholesky process when the square root of a very slightly negative number occurs. At that point you have an approximate partial, low rank decomposition, which might be good enough for your purposes.
– kimchi lover
Sep 3 at 13:03
If the non psd-ness stems only from numerical imprecision, you could simply stop the Cholesky process when the square root of a very slightly negative number occurs. At that point you have an approximate partial, low rank decomposition, which might be good enough for your purposes.
– kimchi lover
Sep 3 at 13:03
If the non psd-ness stems only from numerical imprecision, you could simply stop the Cholesky process when the square root of a very slightly negative number occurs. At that point you have an approximate partial, low rank decomposition, which might be good enough for your purposes.
– kimchi lover
Sep 3 at 13:03
add a comment |Â
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If the non psd-ness stems only from numerical imprecision, you could simply stop the Cholesky process when the square root of a very slightly negative number occurs. At that point you have an approximate partial, low rank decomposition, which might be good enough for your purposes.
– kimchi lover
Sep 3 at 13:03