Questions related to storage, assembly, operations, and other aspects of dealing with sparse matrices, for which only non-zero elements are stored. Questions that do not with sparse matrices directly, but other means of using sparsity should be tagged with [sparse-operator].
Questions tagged [sparse-matrix]
330 questions
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Supernodal vs. Multifrontal Matrix Decompositions
Reading through Tim Davis' book Direct Methods For Sparse Linear Systems, he says that matlab can use a supernodal Cholesky decomposition but never uses a multifrontal Cholesky decomposition. At least when using the backslash operator. By contrast,…
cjordan1
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What is the conventional approach for sparse matrix multiplication?
When you're multiplying sparse matrices against other sparse matrices or dense matrices, what is the conventional approach for each? How are the sparse matrices stored? What does matrix multiplication work?
My understanding is there are several ways…
anonuser01
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vote
1 answer
Consider only triangular part of symmetric matrix for operations
It seems common practice to store only the upper or lower triangular part of a sparse symmetric matrix to save memory. Now I am wondering how, e.g. the SpMV kernel in CSR format is designed and how the matrix elements are accessed which are not…
vydesaster
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Tolerance is not satisfied in eigsh function
I am diagonalizing a sparse matrix of size $153600\times 153600$ via eigsh function. I did not set the tolerance to specific value, so it would be the default value about $2\times 10^{-16}$. However, if I run the same code 3 times, the difference…
Laplacian
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How to use matlab **fft** function or other fast methods to solve a convection-diffusion system quickly?
for a convection-diffusion equation with Dirichlet boundary conditions as follows:
$$-u''+qu'=f$$
Using centered difference for $u''$ and $u'$, we get a linear system
$$Ax=b$$where matrix $A$ is nonsymetric.
Let $H = (A+A')/2,S = (A-A')/2$, we know…
Happy
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BLAS3 in Multifrontal Sparse Decomposition
I wonder how one manages to use BLAS level 3 operations in the multifrontal sparse decomposition algorithm. As far as I understand, the algorithm proceeds as follows:
For each row/column pair, assemble the dense matrix corresponding to
its nonzero…
gTcV
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CSC Sparse Matrices: Why sort row data for Ax=b problems?
I have a matrix in Coordinate format and I will convert it to CSC. As a reference, the format I am using looks like this, but I am not using the pointerE matrix, which I think is superfluous.
My conversion algorithm seems quite slow and I am…
Not a chance
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