Questions tagged [linear-solver]
Referring to methods for solving linear systems of equations.
407
questions
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When does linear system have linearly growing singular values?
Suppose $W$ is a large matrix where $i$th smallest singular value grows as $O(i)$. What kind of matrix can $W$ be?
For instance, this appears to hold for random matrix with IID entries and for lower-...
- 2,695
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vote
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Particular linear systems: sparse matrix + column
I am trying to understand a limitation in a routine in the interval arithmetic software Intlab. From matrices starting from a given size (in my particular problems),...
- 1,077
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votes
1
answer
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Matrix Diagonalization and Computational Requirements
I have some questions about diagonalizing matrices. My interest lies in computing all eigenvalues of a given matrix. To avoid wasting time and improve my research efficiency, I want to understand the ...
- 143
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1
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recommended simple linear solver on gpu
I'm looking for recommendations for a simple GPU linear equation system solver that is a dropin replacement for scipy.linalg.solve. Right now, I'd rather not go the Petsc/TriLinos/Slate route. ...
- 782
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Plasma charge conservation for a multi-Euler system - looking for quasi-linear Riemann solver that also resolves slow contact discontinuity
I am solving a multi-species plasma problem by assigning a set of ideal gas Euler equations to each species, e.g. protons and electrons.
I.e. I am solving the system
$$
\partial_tU_s + \partial_x(F_s) ...
7
votes
3
answers
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views
How large is large for direct solvers?
Let us say I want to solve a large sparse linear system. It is said that iterative solvers should be better than direct solvers in this case. But how large is large? What is the exact threshold beyond ...
- 181
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votes
2
answers
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Cheap way to keep parameter matrices orthogonal during optimization?
TLDR; I can keep matrix variables approximately orthogonal by taking a single gradient step in the direction of "effective rank" of matrix at each step of iterative solver, is there a more ...
- 2,695
0
votes
1
answer
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Weird runtime behavior of `scipy.linalg.solve_triangular` and `trtrs`
I want to understand the time complexity of scipy.linalg.solve_triangular, which calls trtrs from LAPACK under the hood, so I ...
- 181
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votes
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Saddle point system
I am solving a system of the form
$$ \begin{pmatrix}
A & b^T \\
b & 0
\end{pmatrix}
\begin{pmatrix}
x \\ \ell
\end{pmatrix}
= \begin{pmatrix}
c\\
0
\end{pmatrix}
$$
Where $A$ is a symmetric ...
- 1,077
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votes
0
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How conservation of momentum is ensured in (Projected) Gauss-Seidel constrain solver
I'm developing molecular dynamics where my time-step is limited by stiffness of the bonds. I trying to get inspiration from game-engines, where they solve similar problem (hard bond constrains). These ...
- 927
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Population of the coefficient matrix of a linear system Ax=b stemming from the finite differences of an arbitrary geometry
I've been looking into solving a linear system $$Ax=b$$ where $A\in\mathbb{R}$ is the sparse coefficient matrix of size $K\times K$, $b\in\mathbb{R}$ is the right-hand side (i.e., the source term) of ...
- 83
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Solving AU = F using linalg.cg results in 0 iterations
I am working on solving the following PDE: $$\left(\mu_{x}\frac{\partial^{2}u}{\partial x^{2}}+\mu_{y}\frac{\partial^{2}u}{\partial y^{2}}\right)=f(x,y) \tag 1$$
Which is then discretised:
$$- \mu_{x} ...
- 43
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votes
1
answer
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Solving $(I-Q)x={\bf 1}$ for sub-stochastic sparse $Q$ of dimension 5M $\times$ 5M
I have a (right) sub-stochastic CSC sparse matrix $Q$ of dimension 5 million, with 200 million nonzero entries, which is a nonzero percentage of 0.0008%, so it is indeed extremely sparse. It is not ...
- 503
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votes
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Solving for $X$ in $\sum_{a,b} b a^T b^T X a = Y$
Suppose I have $k$ pairs of $(a,b)$ where $a$ and $b$ are vectors in $\mathbb{R}^d$, $Y$ is $d\times d$ and I need least squares solution for $X$ in the following
$$\sum_{(a,b)}^k b a^T (b^T X a) = Y$...
- 2,695
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votes
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answers
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How to use a preconditioner estimated from a subset of data?
Suppose I'm solving $Ax=b$ using row-action method like Kaczmarz for $m\times n$ matrix A with $m\approx \infty$ and have $H_k=\frac{1}{k}A_k^T A_k$ which is an estimate of the Hessian obtained from ...
- 2,695