# Questions tagged [sparse-matrices]

Use this tag for questions regarding sparse matrices, that is matrices with relatively few entries compared to their size. Related: [numerical-methods] and [numerical-linear-algebra].

100 questions
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### Solving a constrained linear system of equations

I want to solve the linear system of equations $$\begin{equation} Ax = b \\ \text{s.t} \quad x \geq 0 \end{equation}$$ The matrix A is a sparse symmetric matrix. What is the best time efficient ...
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### Spark and Mutual Coherence of a matrix: show practical example not using just notation (Compressive Sensing)

I'm reviewing the compressive sensing section of Dr. Elad, and I cannot seem to find a step by step tutorial/process of how to obtain the Spark and Mutual Coherence of a matrix. This is what I've been ...
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### fast linear solvers

I have a linear system $Ax=b$ that is solved in each time step of a code. the point is that matrix $A$ is constant. only the right hand side $b$ is changing every time step. matrix $A$ is sparse with ...
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### Fast way to Invert ADA' when D is a diagonal matrix that changes each iteration?

So I have a statistical learning algorithm in which D is a diagonal matrix that changes each iteration while A stays the same. I'm looking for a fast way to invert ADA' each iteration which ends up ...
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### Relation of SVDs between two particular matrices

Let $A = B - C$ be a very large matrix, where $C$ is a matrix with constant value $C$. Note that in my case $A$ represents an undirected graph adjacency matrix. I need to find the max singular value ...
### How to Mathematically Recover Sparse Signal (Least Squares with ${L}_{1}$ Regularization - LASSO)?
I got this equation for signal recovery by using LASSO: $$\alpha_y =\mathrm{argmin} \left(\| Y - D\alpha \|_2^2 + \lambda^* \|\alpha\|_1\right)$$ Here $D$ is a Dictionary, $Y$ is noisy data signal ...