# Questions tagged [dense-matrix]

Questions about working with or solving equations involving matrices which are known or suspected to have many nonzero elements. Contrast with sparse matrix.

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### Complexity of matrix inversion in numpy

I am solving differential equations that require to invert dense square matrices. This matrix inversion consumes the most of my computation time, so I was wondering if I am using the fastest algorithm ...
• 409
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### Rule of thumb for sparse vs dense matrix storage

Suppose I know the expected sparsity of a matrix (i.e. the number of non-zeros / total possible number of non-zeros). Is there a rule of thumb (perhaps approximate) for deciding whether to use sparse ...
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1 vote
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### Compute all eigenvectors and eigenvalues of small symmetric matrices

My problem is to compute eigenvectors and eigenvalues of a lot of small (n < 30) symetric, positive definite matrices. So far I am using LAPACK's DSYEV. The priority is speed more than accuracy. ...
• 111
1 vote
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### Parallelization of element-wise matrix multiplication

I use Armadillo as an interface to OpenBLAS. In my current program, I have a loop, in which I do multiplications of the form ...
1 vote
265 views

### How is the dense system usually dealt with in spectral method?

Unlike finite element (FEM) or finite difference methods (FDM), where the original PDE is transformed into a sparse linear system, spectral methods return a dense linear system. For a large system, it'...
• 679
1 vote
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### Rearrange a dense distance matrix to a 2x2 non-perfect block diagonal form

I have a distance matrix (square, symmetrical, non-negative, dense). I want to split the objects into two well-connected groups. Mathematically speaking, I want to group (re-arrange) the rows/columns ...
• 131
1 vote
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### How can I reuse the SVD of matrix A to solve LS problems for both A and its transpose via Eigen C++?

If $A\in R^{m\times n}, b\in R^m, c\in R^n$, if I need to solve the least square problems via SVD of $A$ and $A^T$, i.e. I need to solve the least square solutions to following linear systems via ...
1 vote
211 views

### performance comparison between PETSc and SLATE

We want to start a new project to solve a large-scale inverse problem (O(10^6) number of parameters) to invert for subsurface wave speeds. We will use FEM to solve forward and adjoint PDEs. In our ...
1 vote
77 views

### Parallel dense solve with submatrices from mesh refinement with Petsc

For a Bounday Element Method problem I require the solution of a system of linear equations with multiple right-hand sides. Though this is a dense system, I still want to do it via Petsc in parallel. ...
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1 vote
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### Library to solve dense linear system with GMRES

I have a fortran 90 code and I want to solve a dense linear system with GMRES. I would prefer the restarted GMRES with preconditioning. Is there some library that you know of that I could use? Now I ...
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### Discretized matrix from the integral kernel function

Recently, I read a paper [1] and then I want to handle the two-dimensional linear integro-differential equation \begin{equation*} -\triangle u + q\Big(\frac{\partial u}{\partial x} + \frac{\partial u}{...
everyone, I have a question about computational costs for a algorithm. That is: I have two vectors $u_n,\ v_n\in \mathbb{C}^N$, a matrix $A\in \mathbb{C}^{N\times N}$ (can be both sparse and dense) ...