# 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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### Reordering eigenvalues in Schur factorization - MATLAB orschur and LAPACK dtrsen not producing the same results

Disclaimer: I previously posted this on SO, but though it would be more relevant for scicomp. The original post has been deleted. I have been trying to recreate the functionality provided by MATLABs <...
1 vote
63 views

### Calculating camera calibration matrix with Scilab

I'm not entirely sure whether this question belongs here or in DSP but I think this is the proper site. I'm following these videos (first video, second video) to calibrate a camera for photogrammetry ...
132 views

### Is there a way to generate a matrix-free decomposition for a matrix-free operator?

Hypothetical question for some code that I'm writing. Suppose I have an matrix-free linear operator $A$, i.e. the only thing I know about it is the forward action $v \mapsto Av$. For simplicity, let's ...
112 views

### The error propagation in calculating the inverse using a matrix decomposition

I have been trying to calculate the matrix inverse of some large matrix with entries ranging by orders of magnitude. I tried to use the matrix decomposition to simplify the computation, where a matrix ...
108 views

### Is the Hessian of the strain energy of a hyperelastic material positive definite in general

Is the spatial second derivative of the strain energy of a hyperelastic material positive definite in general? If this is not a general property of hyperelastic materials are there techniques for ...
130 views

### Does exact diagonalization of a matrix allow for efficient computation of a Lanczos basis?

Suppose that we are given a large, real-symmetric matrix $L$, which is simply too large to perform exact diagonalization on numerically. If we want to study its spectrum, one tool we can use is the ...
167 views

### Block-Tridiagonal Matrices with tridiagonal blocks

The Setup Using finite differences to discretize the 2d diffusion equation $$\partial_tu=\partial_x\left(A\partial_xu+B\partial_yu\right)+\partial_y\left(B\partial_xu+C\partial_yu\right)$$ we get a ...
17 views

### Nimfa Lsnmf matrix factorization with sparse input: wrong/different result than dense input

I just started using Nimfa and working on a dummy example. I would like to do a matrix factorization (on a matrix for which we do not have all the entries) and I am assuming the following model (which ...
34 views

1 vote
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### QR decomposition with only diagonal elements changing

I have to compute the QR decomposition of a matrix A repeatedly, each time with ONLY diagonal elements changing. Is there an efficient way to accomplish this ...
51 views

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### Numerical Linear Algebra: When to use Direct methods versus iterative methods to solve a linear system - for PDEs in particular

I am reading the Chapra and Canale book on numerical methods, and was working through the chapters on solving linear systems. Now the book goes through direct methods including Gaussian Elimination, ...
72 views

### Does incomplete LU preconditioning improve the asymptotic scaling of Krylov subspace methods?

It is well known that unpreconditioned Krylov subspace methods applied to the finite-difference-discretised Poisson equation with $n$ grid points per direction require $O(n \, |\log(\varepsilon)|)$ ...
1 vote
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### Range of a matrix from its complete orthogonal decomposition

In this StackOverflow answer, @Gokul has shown how to get a basis of the kernel of a matrix with the help of the 'Eigen' function CompleteOrthogonalDecomposition. ...
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1 vote
I need to solve many least squares problems with the following matrices: $$\pmatrix{ R \\ D_i }$$ where $R$ is upper triangular and $D_i$ is diagonal. $R$ is the same for all the problems, while $... 0 votes 2 answers 386 views ### Reorder eigenvalues in Schur factorization in descending order In this command: [US,TS] = ordschur(U,T,select) what should replace the select to rearrange the eigenvalues in descending ... 1 vote 1 answer 256 views ### How can I get Cholesky decomposition from eigenvalue decomposition? I have $$S = QLQ^T$$ I know$Q$,$L$,$Q^T$. How can I get the$R$and$R^T$for the Cholesky decomposition$S=R^TR\$? 