Questions on the linear algebra functionality of Mathematica.
2
votes
2answers
374 views
Can RowReduce work in this matrix?
The matrix $Q$ with dimensions $n\times2*n*m$ is structured by
$$Q=[B|AB|\cdots|A^{2*n-1}B]$$
where $Q$ is an augmented matrix built from a $3\times3$ matrix, $A$, and a $3\times2$ matrix, $B$.
I ...
8
votes
0answers
178 views
More efficient matrix-vector product
Dear mathematica users,
In my present research I am faced with a real dense $n\times n$ matrix $A$ where $n \geq 3000$ (hopefully even more). The coefficients of this matrix are fixed, but I will ...
7
votes
0answers
168 views
How to produce the ILU0 or ILUT as stand-alone procedures on sparse matrices?
Mathematica uses the ILU0 procedures automatically to precondition large sparse linear systems; e.g.
...
6
votes
0answers
103 views
Calculating the rank of a huge sparse array
By virtue of the suggestion in my previous question, I constructed the sparse matrix whose size is $518400 \times 86400$, mostly filled with $0$ and $\pm 1$. Now I want to calculate its rank.
Since ...
6
votes
0answers
228 views
Inverse of a large sparse Hermitian block matrix
I am looking for a method (if it exists) for the inverse of a large sparse Hermitian block matrix.
The off diagonal sparse matrices, named δ are 4x4, and they have ...
4
votes
0answers
155 views
NullSpace[_, Method->“OneStepRowReduction”] is sometimes wrong; how can I work out when this happens?
(This is on MMA 7.0.1.0 on OS X)
I've just found a large matrix m for which NullSpace[m] and ...
3
votes
0answers
122 views
LeastSquare Solution for the Continuous Time Lyapunov Equation
I have been working with a problem which involves solving the continuous time Lyapunov equation
$$A R + R A^\top = G$$
for the symmetric positive definite matrix $R$. Here $A$ is real, invertible ...
2
votes
0answers
54 views
Fast calculation of commute distances on large graphs (i.e. fast computation of the pseudo-inverse of a large Laplacian / Kirchhoff matrix)
I have a large, locally connected and undirected graph $G$ with $\approx 10^4$ vertices and $\approx 10^5$ to $\approx 10^6$ edges. Moreover I can bound the maximum vertex degree as $Q_{max}$. I ...
2
votes
0answers
77 views
Evaluating a function on permutations of its arguments
Say I have a function "temp" of $n+1$ variables, $y,z1,z2,z3,...,zn$. I want to test if my function has certain symmetries like swapping $y$ with square of any $z$, swapping any two of the zs, ...
1
vote
0answers
71 views
Nontrivial solutions of equation
Here, I have one problem in finding nontrivial solutions of a system of equations. I want to choose one variable, for example X1 and to get solutions of X2(X1) and X3(X1). It is not difficult when I ...
1
vote
0answers
94 views
How to express this output in the form $X=A.x$?
This problem arose in my stereo vision project.
I have two matrices:
$$
A = \left(
\begin{array}{ccc}
\text{x1}*\text{p131}-\text{p111} & \text{x1}*\text{p132}-\text{p112} & ...
1
vote
0answers
167 views
Matrix algebra vs. PrincipalComponents and Varimax/Oblimin
Using matrix algebra I can calculate loadings and scores from the covariance matrix (data matrix is column centered):
...
1
vote
0answers
132 views
Parallel linear algebra with arbitrary precision
Is it possible to do parallel linear algebra with arbitrary precision within Mathematica (in a simple manner, as is done for the machine precision)?
0
votes
0answers
109 views
6x6 matrix NullSpace
I'm working with a 6x6 matrix. Whenever I try to find the NullSpace and FullSimplify it, I get the error
No more memory ...
0
votes
0answers
62 views
Inverse problem of Eigenvalues in DSolve
For my graduation exam I must prepare system of equations to satisfy some specific conditions. I have solutions, output 2, but I need equations eq11 and eq22. So here is an example.
...
