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Is there any efficient algorithm to compute the determinant of a sparse matrix? 

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July 19, 2012, 15:42 
Is there any efficient algorithm to compute the determinant of a sparse matrix?

#1 
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Hector Redal
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Hello,
I would like to know if there is any efficient way to compute the determinant of an sparse matrix? Kind regards, Hector. 

July 20, 2012, 00:36 

#2 
Senior Member

LU decomposition for the sparse decomposition. the determinant can be abtained by sum the digonal of mattrix.


July 20, 2012, 06:35 

#3  
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Hector Redal
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Quote:
Thanks for your response. One more question: Do you know where I can find LU decomposition for sparse matrix (article, reference)? Best regards, Hector. 

July 20, 2012, 06:55 

#4 
Senior Member

http://www.cise.ufl.edu/research/sparse/CSparse/
what is your matrix dimension? if your matrix dimension is not very large, i think we can use the traditional computational method to compute it. 

July 20, 2012, 07:09 

#5  
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Arjun
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Quote:
http://books.google.de/books/about/D...EC&redir_esc=y One good book that also provides source code (i think). Remember that LU factorization for sparse matrix may not be that sparse. Whether ILU is sufficient for your need or not is what shall think. 

July 20, 2012, 08:53 

#6 
Senior Member

no ilu is incomplete lu , it is an approximation.
try to use lapack http://www.netlib.org/lapack/double/dgetrf.f * DGETRF computes an LU factorization of a general MbyN matrix A * using partial pivoting with row interchanges. 

July 20, 2012, 09:00 

#7  
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Arjun
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Quote:
I am pretty sure what ILU is. I am also sure that calculating LU from sparse matrix is not efficient thing to do. Thats why I said think if ILU is sufficient for the needs. 

July 21, 2012, 03:26 

#8  
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Hector Redal
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Quote:
Thank you very much for the information you had provided to me. This is by far more than I needed. Thanks. The matrix dimension for the LU decompostion varies from 2 to 10. This is the range I need. I am developing a software for CFD using the finite element method, and for calculating the element matrices for the algorithm, I need the determinant of this matrices. As mentioned before, I am thinking of using the LU decomposition for calculation of the determinant. 

July 21, 2012, 03:44 

#9  
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Hector Redal
Join Date: Aug 2010
Location: Madrid, Spain
Posts: 153
Rep Power: 8 
Quote:
Thanks for the information. I agree with you that LU factorization may not be an sparse matrix. The need for LU factorization is to compute the determinant of the sparse matrix. That's the reason why I need it. Maybe, as you state, it is sufficient to compute the iLU for estimation of the determinant. This is a good point to think about. Thanks again. 

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