# 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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### Big errors while calculating Complex Cholesky Factorization

I am using my own Routine to calculate the Cholesky-Factorization of a complex, positive definite symmetric Matrix. My Code Looks like this: ...
503 views

### Difference between fast and normal Givens Rotations?

would someone be so kind as to explain me the difference between the ordinary givens-rotation and the fast givens-rotation? I know that the fast givens Rotation reduces the Count of operations to ...
107 views

### Is there an efficient $O(n^2)$ way to get the eigen decomposition given a LDL factorization?

Let's say I have a LDL factorization of a matrix A. Is there an efficient $O(n^2)$ way to get the eigen decomposition of A given it's LDL factorization? Is there a more efficient way, in case L and ...
119 views

### Evaluating a quadratic form with an inverse of a sparse PD matrix, comparison between using the inverse vs using a Cholseky decomposition

I have the following quadratic form I need to evaluate: $x^T A^{-1} y$, where $A$ is a sparse positive definite matrix, $x, y$ are sparse vectors. Now assume that I am given for free both $A^{-1}$ ...
135 views

### What is the computational cost of using complex numbers in contrast to real numbers in matrix operations, e.g. $LU$ or $LDL^T$ factorizations? [duplicate]

I am curious about how much one loses in terms of computational cost when complex numbers are used instead of real numbers? I guess the number of floating-point operations and memory doubles, but I ...
853 views

### Solve Ax=B where B is a matrix in parallell

I try to solve the problem $Ax=B$ where $A$ is a large sparse $n\times n$ matrix, and $B$ is a dense $n\times m$ matrix (here $n=754850$ and $m=182$). The backslash operator yields correct solution (<...
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### What is the cost of factorization for one-dimensional sparse problems?

In Golub and Van Loan's book, Matrix Computations, page 606, it is stated that: With standard discretizations, 2-dimensional problems can be solved with $O(n^{3/2})$ work and $O(n \log{n})$ fill-...
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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, ...
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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 ...
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### Can anyone give me some suggestions about optimize my Matlab codes?

recently, I try to write a Matlab codes to implement a sparse approximation inverse factorization method proposed by M. Benzi in his paper http://www.mathcs.emory.edu/~benzi/Web_papers/ainv.pdf this ...
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### Compiling HSL_ME57 and interfacing with C code

Has anyone here had any success (or at least tried) compiling the HSL_ME57 (or similar such as MA57, etc.) matrix factorization libraries? Do any C wrappers exist for the Fortran function calls? I'm ...
136 views

### Efficient way to do congruent transformation using matrix inverse?

I know a square self-adjoint matrix $S_{vv}$ and I want to find: $S_{rr} = HS_{vv}H^{\dagger}$ where $\dagger$ denotes conjugate transpose. I do not know $H$ but I do know $H^{-1}$. What is the ...
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### why Lapack routine dgesv doesn't solve this?

Suppose I have the following 3 by 3 matrix: p<-3 X<-matrix(1/p,p,p) --$\pmb X$ is just a $p$ by $p$ matrix where every entry is $1/p$. Now I want to solve ...
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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### Robust algorithm for $2 \times 2$ SVD

What is a simple algorithm for computing the SVD of $2 \times 2$ matrices? Ideally, I'd like a numerically robust algorithm, but I'll like to see both simple and not-so-simple implementations. C code ...
190 views

### Non-negative matrix factorization for sparse input

Looking for some software to deal with 50kx50k sparse matrix applying non-negative matrix factorization. Do you know any?
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### Missing nonzeros in U matrix computed by SuperLU

On page 18 of SuperLU's user guide, the following sample input matrix A is given: ...
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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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### Computing smallest eigenvectors of a sparse matrix, having its inverse

I'm a bit confused by the vast amount of literature on solving eigenvalue problems. I have a sparse (large) matrix which I have already factored (by Cholesky or LDU). I would like to compute few ...