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Questions tagged [block-decomposition]

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3
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1answer
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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 ...
0
votes
0answers
254 views

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 $\mathbf{A}$...
6
votes
0answers
122 views

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 ...
5
votes
2answers
280 views

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} ...
-1
votes
1answer
59 views

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 ...
7
votes
1answer
4k views

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 ...
3
votes
2answers
784 views

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 $P$, $PAP^T$ ...
5
votes
2answers
474 views

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). ...
3
votes
1answer
849 views

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 ...