# Questions tagged [matrix-free]

For questions about matrix-free methods, which only require computing matrix-vector products, rather than storing the whole matrix explicitly.

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### Applying matrix square root inverse in matrix-free regime

Let $A$ be a large symmetric positive definite matrix, and suppose that we can efficiently apply $A$ and have a fast solver to apply $A^{-1}$, but we do not have access to the matrix entries for ...
• 3,143
705 views

### Matrix free finite elements method for visualization in process tomography

I am Computer Scientist and now I am interested in matrix multiplication on GPUs. My research are focused on matrix free finite elements method where I multiply sparse matrix. Sparse matrix could ...
• 95
292 views

### Matrix-free FEM references

I've seen that many people are using matrix-free fem codes in my community (mechanical engineering). I have to admit that I googled a bit and I didn't manage to find a good reference for the subject. ...
• 405
167 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 ...
• 141
216 views

### High quality constrained optimization C++ library with matrix free second order solver?

I'm working with large scale constrained optimization problem. Some of my constraints can be non linear. Currently i'm using IPOPT. Quality is good by my Hessian computation too slow. It seems that i ...
• 225
129 views

### Parallel, matrix-free estimate of the trace

What would be the best way to estimate the trace of a large, distributed matrix, if one only know its action on a vector throug a parallel "matvec" routine? In the application I am interested in, the ...
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### Memory/speed tradeoff for many small matrix inverses

Problem In the case of a finite element code, I have many small (order of 30x30) matrix inverses (or LU factorizations), one per finite element. These matrix inverses never change and must be applied ...
• 672
1 vote
744 views

### Implementation of the Jacobian-free Newton method

In my calculation (of a simple heat equation, for testing) using the Newton method, I tried to replace the full Jacobian matrix with an approximation vector, i.e. replacing $J$ in J(u)\delta u=-F(u)...
• 563
1 vote
450 views

### Solver library for matrix-free linear equation system

I will have to solve a large linear system. I'm now looking for a solver that works "matrix-free" (So that I just have to specify a matrix-vector product, but not the matrix). As far as I understand (...
• 1,463
1 vote
I have an equation of the form $J^Te=f$, where $e$ and $f$ are known vectors and $J$ is an unknown matrix. How can I efficiently compute $J^T(JJ^T)^{-1/2}e$ ? My motivation to address this problem ...