Questions tagged [matrix-factorization]

Decomposition of a matrix into a product of matrices with special properties. Common matrix factorizations include LU, QR, SVD, and Cholesky.

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Algorithm to factorize matrix whose many rows are already of upper triangular form?

I have a matrix whose many rows are already in the upper triangular form. $$\begin{bmatrix} x_{11} & x_{12} & x_{13} & x_{14} & x_{5} \\ 0 & x_{22} & x_{23} & x_{...
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2answers
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Factoring the sum of two matrices

Given \begin{equation} A_i=B+C_i \end{equation} where $A_i$,$B$ and $C_i$, $i=1,\dotsc,N$ are large square matrices, $B$ is symmetric, $C_i$ are zero matrices aside for a square block on the diagonal. ...
6
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2answers
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Sparse Incomplete Cholesky

I'm looking for an efficient, multicore, library to do incomplete cholesky (possibly modified). Many ILU code exists, but I can't find much about IC except in PETSC or Pastix. Could some of you drop ...
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1answer
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Is the bandwidth of indefinite A equal to its factor L in LDL^T?

In George, Liu, and Ng's book Computer Solutions of Sparse Linear Systems, it has been shown that bandwidth of $A$ is equal to bandwidth of its factors in $LL^T$.(section 4.3) However, I guess this is ...
4
votes
1answer
159 views

Factorization for reweighted least squares

I am solving a problem using an iteratively-reweighted least squares method: http://en.wikipedia.org/wiki/Iteratively_reweighted_least_squares Essentially this requires solving a number of least-...
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Is there an upper bound for fill-ins for indefinite triangular factorization?

For $A=LU$, or $A=LDL^T$ factorization, bandwidth is preserved when there is no pivoting. This is true even for indefinite A, see question. However, when there is pivoting band structure is destroyed, ...