Questions tagged [block-decomposition]
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14
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Viable algorithms for efficiently solving a block matrix system with non-uniform sparsity structure
I am trying to use Newton's method to get a stationary solution for a system of equations of the following form:
$$
\begin{Bmatrix}
\frac{\partial x}{\partial t} \\
0
\end{Bmatrix} = \begin{Bmatrix}
f(...
- 81
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56
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Number of words that a processor can handle for PMMM
The PMMM which stands for parallel matrix-matrix multiplication essentially accelerates the algorithm of the matrix-matrix multiplication of two matrices $A$ and $B$ both of size $n$ so that $C:= AB$. ...
- 297
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498
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What is the algorithm to convert an adjacency matrix to a block diagonal structure?
I'm a little at loss as to what my supervisor meant by the "hierarchical block decomposition" of a matrix, but the goal is to put a sparse symmetric adjacency matrix into a block diagonal structure to ...
- 151
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2
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417
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Block-matrix: optimal fill-in reduction for LU factorization
Consider a square $N \times N$ block-matrix $\mathbf{A}$, where each $n \times n$ block $\mathbf{A}_{ii}$ is either a dense block or a zero-block. So, $N$ denotes the number of blocks, $n$ denotes the ...
- 8,552
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Block-matrix SVD and rank bounds
Assume, we have an $m\times n$ block matrix $M=\left[\begin{array}{c c}A&C\\B&D \end{array}\right]$, where
$A$ is an $m_1 \times n_1$ matrix of rank $k_A$.
$B$ is an $m_2 \times n_1$ matrix ...
- 8,552
0
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444
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Cholesky factorization of a block matrix
Let a Matrix $\mathbf{Y=[A\;b;b^T\;}d]$, where $d$ is a scalar, and $\mathbf{b}$ is a vector.
How to find the cholesky factorization of $\mathbf{Y}$ if i know the cholesky factorization of $\mathbf{A}$...
- 123
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What strategies / decompositions would be useful to solve the following linear system repeatedly if I only care about time to solution?
Let $A\in \mathbb{R}^{n\times n}$ be symmetric positive semidefinite, and $B\in \mathbb{R}^{n\times n}$ be symmetric positive definite. Suppose $B$ is block diagonal so it is easy to invert. (We ...
- 1,000
5
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2
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367
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Preconditioning symmetric Schur complement
Consider a $2\times 2$ block matrix and a linear system of equations associated to it:
\begin{equation}
\begin{pmatrix} - A & B \\ B^t & C \end{pmatrix}
\begin{pmatrix} x \\ y \end{pmatrix}
...
- 3,570
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-1
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Is it possible to find a formula for a set of number from the result? [closed]
I have these two sets of number, I also have a result. Is it possible to compute
the relation between them so that I can figure out how the result is generated ?
for example I have :
Set A=4 6 12 25 ...
- 1
8
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cholesky factorization of block matrices
I have a block matrix (either 2x2 blocks or 3x3 blocks) which is the covariance matrix for a joint space of two or three multivariate normal variables. ie
...
- 183
3
votes
2
answers
1k
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Solving sparse matrix systems which can be reordered to block diagonal form
I have a class of matrices $A$ which are created by a domain decomposition method. Each matrix represents several subproblems of equal size, and I know that for some permutation matrix $P$,
$PAP^T$ ...
- 824
5
votes
2
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549
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What does symmetrize mean? (imposing multifreedom constraints to stiffness matrix)
I have a small FEM implementation program. And I want to add imposing multifreedom constraints (MFC) feature to it. The theory of master-slave method is given here (page 10 for general case).
...
- 501
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988
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Is a checkerboard block decomposition of a matrix useful when solving a linear system with a parallel conjugate gradient method?
According to these lecture notes, a checkerboard block decomposition should exhibit better scalability when applied to parallel matrix-vector multiplication (presumably because of greater cache hit ...
- 11.9k