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No progress in Jordan decomposition of a symbolic matrix

bananas consult
Posted 3 years ago

Hello and thanks for reading my first post in this amazing community.

I'm an econometrics student and for the purpose of my master thesis from the area of stability in economic modelling I'm performing an Jacobian decomposition of a 5x5 symbolic matrix.

The matrix includes quite large expressions that include 15 variables and the file has about 1.4 MB. The decomposition performed with the command JacobDecomposition[mat] is making no progress.

Is there any way to perform the decomposition in accepting time? It has taken about a day and a half, in comparison to the operations like matrix multiplication that are done in a couple of seconds.

I attached the file with code, I hope this will work.

Attachments:
Matrix.nb
POSTED BY: bananas consult
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Cross-posted to MSE here
POSTED BY: Daniel Lichtblau

I'm still looking for the solution. I considered your idea of rationalizing numbers but the size of expressions is very large, as it can be seen - this time I attached the original matrix in the post above.

I'm thinking of doing the decomposition in steps perhaps, like the Cholesky decomposition that can be performed in 3 steps by introducing intermediate variables.
POSTED BY: bananas consult

I would suggest trying Eigensystem to see if that completes faster. If the eigenvalues are distinct (I believe they will be) then one can get the Jordan decomposition from the eigensystem.
POSTED BY: Daniel Lichtblau

It sounds good, will try.
POSTED BY: bananas consult

Hi again,

I'm not sure what is the problem, but after 24 hours the process is still running. It's using <10 % of processor, but about 90 % of RAM (8 GB) so I'm thinking fixing this hardware constraint could be a way forward.

Another question, could command Roots and setting characteristic polynomial to zero be any faster?

I also realized my 5x5 matrix has a rank of 4, so this could be slowing up the process, as you indicated on Mathematica Stackexchange.
POSTED BY: bananas consult
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