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Questions tagged [svd]

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.

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30 votes
11 answers
11k views

Robust algorithm for $2 \times 2$ SVD

What is a simple algorithm for computing the SVD of $2 \times 2$ matrices? Ideally, I'd like a numerically robust algorithm, but I'll like to see both simple and not-so-simple implementations. C code ...
lhf's user avatar
  • 966
11 votes
3 answers
2k views

What's the current state of the art regarding algorithms for the singular value decomposition?

I'm working on a header-only matrix library to provide some reasonable degree of linear algebra capability in as simple a package as possible, and I'm trying to survey what the current state of the ...
gct's user avatar
  • 211
10 votes
2 answers
1k views

How much regularization to add to make SVD stable?

I've been using Intel MKL's SVD (dgesvd through SciPy) and noticed that results are are significantly different when I change precision between ...
Yaroslav Bulatov's user avatar
13 votes
0 answers
719 views

Fast Eigenvalue and SVD Solver for Structured Matrices

I am looking for a fast Eigenvalue and SVD solver for small dense structured matrices (Hankel and Toeplitz). I have searched for efficient implementations in libraries like MKL but I am not able to ...
Sai Venkat's user avatar
8 votes
4 answers
5k views

Incremental SVD implementation in MATLAB

Is there any library/toolbox which has implementation of incremental SVD in MATLAB. I have implemented this paper, it is fast but does not work well. I tried this but in this also error propagates ...
Parag's user avatar
  • 201
8 votes
3 answers
934 views

What should be the criteria for accepting/rejecting singular values?

I am solving a system using singular value decomposition. The singular values (before scaling) are: ...
drjrm3's user avatar
  • 2,129
6 votes
1 answer
972 views

Inverse iteration to find the null singular vector of a rank-deficient matrix

I have an $n \times n$ unsymmetric matrix $A$ that results from the discretization of an ill-posed Poisson problem, and thus is rank-deficient with null space of dimension one. I want to compute just ...
Sumedh Joshi's user avatar
4 votes
1 answer
360 views

Analytic formula for leading eigenvector of $uu^T + vv^T$?

Let $u$ and $v$ be nonzero column vectors of size $n$ and consider the $n \times n$ positive-definite matrix $A:=uu^T + vv^T$. In this post https://math.stackexchange.com/a/112201/168758, the ...
dohmatob's user avatar
  • 175
3 votes
2 answers
2k views

SVD of large block-hankel matrix

I am trying to do SVD of a large block-hankel matrix for model order reduction (Low rank approximation). However, I quickly run into memory issues in forming the large Block-Hankel matrix and CPU ...
Dr Krishnakumar Gopalakrishnan's user avatar
3 votes
1 answer
756 views

singular value decomposition of a 2 x 2 complex matrix

This should be easy, but... I would like to express the singular value decomposition of a 2 x 2 complex matrix $A$ as function of its coefficients $A_{ij}$. In "closed form", no intermediate values, ...
Ali K's user avatar
  • 31
2 votes
1 answer
1k views

Matlab - Fast Computation of Truncated SVD / PCA

I'm working with a Matlab codebase wherein I'm attempting to solve A*c = b by approximating the (square) matrix A with its ...
davewy's user avatar
  • 145
0 votes
1 answer
90 views

Analytic formula for $\arg\max_{\|z\|_\infty \le 1}z^T A z$, where $A=uu^T+vv^T$

Let $u$ and $v$ be column vectors of size $n \gg 1$ (not both zero), and consider the matrix $A:=uu^T+vv^T$ Question What is an analytic formula for $\arg\max_{\|z\|_\infty \le 1}z^TAz=\arg\max_{\|z\...
dohmatob's user avatar
  • 175
0 votes
1 answer
787 views

ZGETRF and ZGETRS from MKL - zgetrf fails and still zgetrs works?

I have a large system of equations $$Ax=b$$ and I know matrix $A$ and right-hand side vector $b$. I'm using MKL to solve this system. The matrices are complex. I have used the general solver ...
lovis's user avatar
  • 137