Questions tagged [block-decomposition]

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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(...
1 vote
0 answers

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 $C:= AB$. ...
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3 votes
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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
7 votes
2 answers

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
4 votes
1 answer

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 votes
0 answers

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
6 votes
0 answers

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 votes
2 answers

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} ...
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1 vote
0 answers

Matlab: why I am getting the block diagonal form of this antisymmetric matrix always as zero?

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-1 votes
1 answer

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 votes
1 answer

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

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 answers

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
3 votes
1 answer

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 ...
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