# 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].

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### How to update/recalculate the inverse of matrix after changed one element's value?

I have a large sparse matrix A and have gotten its inverse matrix inv(A) . Then I need to change an element value to get a new ...
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### Universal Approximation Theorems for Sparse Networks

It is well-known, as shown in Hornik's papers, that feed-forward neural networks are dense in the spaces of continuous functions (uniformly on compacts) and the spaces of $L^p$ functions (for suitable ...
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### Eigenvalues of sparse matrix

I want to calculate the eigenvector corresponding to the $0$ eigenvalue of a large, sparse singular matrix. However, if I try eigs(A,1,'smallestabs'), MATLAB has an ...
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### Eigenvector of large sparse stochastic matrix

I have a large sparse matrix corresponding to a system of master equations for a continuous-time Markov chain. It's approximately $500,000 \times 500,000$, with a density of around $10^{-6}$. Is ...
2answers
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### Diagonalization of very large (but very simple) sparse matrix

I have a $10^5 \times 10^5$ matrix and I need its smallest eigenvalue (not the the smallest in absolute value, but actually the lowest) and the associated eigenvector (I know the eigenvalue to be non-...
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### Need to solve a linear system with a sparse n x n matrix

I am developing an application in C# language — an electric simulator that uses the node-voltage method in the AC frequency domain. I need to solve large systems of linear equations (over $\mathbb C$)...
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### How to generate random sparse unitary with given density?

For my research, I need to generate sparse (complex-values) unitary matrices at random from a uniform distribution. It is not a problem for me to generate the generic unitary matrices using, e.g., ...
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### compute $C = AB^{-1}A^T$ without inverting B

Is it possible to compute $C = AB^{-1}A^T$ without computing the inverse of $B$ explicitly? A is $n \times m$ matrix. B is $m \times m$ matrix ($m \gg n$). Thus $C$ is much smaller than $B$. In the ...