Questions tagged [linear-algebra]
Questions on the algorithmic/computational aspects of linear algebra, including the solution of linear systems, least squares problems, eigenproblems, and other such matters.
7
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Preconditioner Implementation with matrix-free methods (sparse iterative solvers)
How can I define preconditioners (SPILU,SPAI, etc.) for sparse iterative methods (TFQMR,GMRES,CGS, etc.) for the matrix-free left-hand side? I defined Ax=b using matrix-free A (with LinearOperator and ...
- 1
5
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2
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476
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Solving a generalised eigenvalue problem with non-square matrices
I need to solve a generalised eigenvalue problem of the form
$$A\mathbf{x}=\lambda B \mathbf{x}$$
where $A$ and $B$ are $m \times n$ complex matrices, that are not symmetric with $m>n$.
I am aware ...
- 51
0
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1
answer
59
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How to properly use ARPACK's dsaupd and dseupd?
In Rust, I am trying to solve an eigendecomposition problem through ARPACK. I made the following subroutine for this purpose:
...
- 273
2
votes
1
answer
69
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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-...
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What's the most computationally efficient implementation of Kalman Filter
I know there are many formulations of the Kalman Filter. A few I can name are:
Classical Covariance Form
Informational Filter Form
Square-Root Form or Factor Form
But somehow it's hard for me to ...
- 435
0
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1
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81
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optimize this python code that involves matrix inversion
So I have this line of code that involves a matrix inversion
X = A @ B @ np.linalg.pinv(S)
$A$ is an $n$ by $n$ matrix, $B$ is an $n$ by $m$ matrix and $S$ is an $...
- 127
4
votes
1
answer
103
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How can I efficiently find an anti-symmetric generator of a special orthogonal matrix?
Given a special orthogonal matrix $O$ (i.e: $OO^T = 1$ and $\det(O) = 1$), I am trying to efficiently find a matrix $X$ such that $O = e^X$ and $X = -X^T$ using Python (NumPy & SciPy).
One obvious ...
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