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Results tagged with svd
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user 4405
Singular Value Decomposition (SVD) is a decomposition (factorization) of rectangular real or complex matrix into the product of a unitary rotation matrix, a diagonal scaling matrix, and a second unitary rotation matrix.
2
votes
Why is Matlab's SVD faster on skinny matrices than on fat matrices?
(Another related question to which I don't have a good answer is "why doesn't LAPACK's SVD routine DGESVD accept a TRANS parameter, unlike several others?".) …
- 12.5k
6
votes
Accepted
Finding the $i$-th largest eigenvalue of a matrix
No, there is nothing, as far as I know, unless you know approximately the location of these eigenvalues. As for methods that can compute a subset of the spectrum of a matrix, I know only of methods th …
- 12.5k
4
votes
Asymptotic complexity of fixed-rank SVD
You can now compute and SVD of $R$, and use it to piece back the factors with a few matrix products with cost $O(\max(m,n)k^2)$. …
- 12.5k
3
votes
Accepted
Whitening transformation does NOT return a unit covariance matrix
As a final note, as someone who works in numerical linear algebra, I can't avoid pointing out that svd($XX^T$) is not the most numerically stable way to compute the singular values and vectors of $X$, …
- 12.5k
5
votes
My Complex Matrix SVD is Correct according to rule A = USV' but Wrong according to Matlab or...
This should not be possible. $U$ and $V$ may be non-unique in the case where there are repeated singular values, but $s$ must be unique, since it is the sorted list of eigenvalues of $A^*A$ and eigenv …
- 12.5k
10
votes
Accepted
Why are all eigen solvers iterative?
There is simply no closed-form expression in terms of the four operations and radicals for the eigenvalues of a matrix greater than $4\times 4$.
This follows from the facts that (1) there are polynomi …
- 12.5k
9
votes
Accepted
Poor SVD reconstruction of singular matrix
Algorithms for the SVD, as more or less every classical linear algebra algorithm based on orthogonal transformations, are normwise backward stable, i.e., it should be guaranteed that $\frac{\|USV^* - A …
- 12.5k
3
votes
accuracy problem for a null space calculation on a sparse rectangular matrix
You mention in a comment that the relative residual norm(Bm*Lrm) / norm(Bm) / norm(Lrm) is of the order of machine precision.
So everything is working as intended, it seems. Essentially, the computed …
- 12.5k