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I'm also trying to solve a similar problemsimilar problem: transform a matrix that is not positive definite into a positive definite one for then applying a Cholesky Decomposition.

I'm also trying to solve a similar problem: transform a matrix that is not positive definite into a positive definite one for then applying a Cholesky Decomposition.

I'm also trying to solve a similar problem: transform a matrix that is not positive definite into a positive definite one for then applying a Cholesky Decomposition.

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I'm also trying to solve a similar problem: transform a matrix that is not positive definite into a positive definite one for then applying a Cholesky Decomposition. 

The best way to solve the problem would be change the equations to use a generalized robust Cholesky with pivoting, unluckilydecomposition $LDL^T$ that doesn't take the square root of the matrix (see 1 and 2). This way, I don't know how to do thisyou might be able to my problemwork directly with the non-definite matrix.

ButAnyway, here's a simpler method to convert"convert" the matrix to a positive definite one and it seems to be better at reconstructing the original matrix than the one you pointed out:.

TestResults of a test with a matrix that is already positive definite, so the matrix should be preserved:

I'm also trying to solve a similar problem. The best way to solve the problem would be change the equations to use a generalized robust Cholesky with pivoting, unluckily, I don't know how to do this to my problem.

But here's a simpler method to convert the matrix to a positive definite one and it seems to be better at reconstructing the original matrix than the one you pointed out:

Test with a matrix that is already positive definite:

I'm also trying to solve a similar problem: transform a matrix that is not positive definite into a positive definite one for then applying a Cholesky Decomposition. 

The best way to solve the problem would be change the equations to use a Cholesky decomposition $LDL^T$ that doesn't take the square root of the matrix (see 1 and 2). This way, you might be able to work directly with the non-definite matrix.

Anyway, here's a simpler method to "convert" the matrix to a positive definite one and it seems to be better at reconstructing the original matrix than the one you pointed out.

Results of a test with a matrix that is already positive definite, so the matrix should be preserved:

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I'm also trying to solve a similar problem. The best way to solve the problem would be change the equations to use a generalized robust Cholesky with pivoting, unluckily, I don't know how to do this to my problem.

But here's a simpler method to convert the matrix to a positive definite one and it seems to be better at reconstructing the original matrix than the one you pointed out:

Test with a matrix that is already positive definite:

Before:

   1.00114  0.0015438  0.0055613  0.0083755  0.0114398  0.0271191
 0.0015438    1.00209 0.00751505  0.0113179  0.0154588  0.0366463
 0.0055613 0.00751505    1.02707  0.0407709  0.0556878   0.132013
 0.0083755  0.0113179  0.0407709     1.0614  0.0838676   0.198815
 0.0114398  0.0154588  0.0556878  0.0838676    1.11455   0.271555
 0.0271191  0.0366463   0.132013   0.198815   0.271555    1.64375

After, using the method you mentioned:

         1 0.00154131 0.00548439 0.00812499  0.0108298  0.0211402
0.00154131          1 0.00740762  0.0109742  0.0146276  0.0285536
0.00548439 0.00740762          1   0.039049  0.0520486   0.101601
0.00812499  0.0109742   0.039049          1  0.0771088   0.150519
 0.0108298  0.0146276  0.0520486  0.0771088          1   0.200628
 0.0211402  0.0285536   0.101601   0.150519   0.200628          1

After using the simpler method:

   1.00114  0.0015438  0.0055613  0.0083755  0.0114398  0.0271191
 0.0015438    1.00209 0.00751505  0.0113179  0.0154588  0.0366463
 0.0055613 0.00751505    1.02707  0.0407709  0.0556878   0.132013
 0.0083755  0.0113179  0.0407709     1.0614  0.0838676   0.198815
 0.0114398  0.0154588  0.0556878  0.0838676    1.11455   0.271555
 0.0271191  0.0366463   0.132013   0.198815   0.271555    1.64375

Test done using C++ Eigen library with double precision.