Share Your Experience: Take the 2024 Developer Survey

# 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.

17 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
718 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 ...
• 241
215 views

### SVD computation with "initial guess"

Suppose I have some matrix A whose SVD I know. Now, I am given B which is A plus some small ...
• 599
46 views

### Solving linear system and obtaining operator norm

I need to solve a linear system of the form $(\mathrm{Id} + \mathbf{J})\mathbf{x} = \mathbf{b}$ for $\mathbf{x}$ and I also need to compute the operator norm of $\mathbf{J}$ (i.e. the largest singular ...
• 183
388 views

### Computing Singular Value Decomposition of small ($4\times 4$) matrices

I need to compute the Singular Value Decomposition (SVD) of many $4 \times 4$ matrices. I'm looking for SVD algorithms specialized for small matrices. I've read that the ...
• 131
758 views

I need to solve the following equation: $$\begin{pmatrix} \frac{\omega^2}{c^2}\varepsilon_x-\mu_z^{-1}k_y^2-\mu_y^{-1}k_z^2 & \mu_z^{-1}k_xk_y & \mu_y^{-1}k_xk_z\\ \mu_z^{-1}k_xk_y &\... • 217 2 votes 0 answers 211 views ### Generalized eigenvalue with null space Define S\in\mathbb{R}^{n\times n} as$$S:=H+Q^\top V^{-1} Q.$$H,V are positive semidefinite. Here, H, Q, and V are large, dense matrices but they are structured: I can write code for ... • 1,341 2 votes 0 answers 62 views ### Optimal ordering in Jacobi SVD algorithm In Jacobi SVD algorithm as given here every pair of columns of the matrix is orthogonalized until convergence. I want to know that how does the order of selection of the pair of columns affect the ... • 121 2 votes 0 answers 32 views ### Choosing suitable polynomial degree based on information in advection stencil I'm working on a finite volume advection scheme for unstructured meshes which uses a multidimensional polynomial weighted least squares fit for interpolating from cell centres onto faces. In 2D, the ... • 222 2 votes 0 answers 234 views ### Using Centroid decomposition instead of SVD This paper says centroid decomposition (CD) is an approximation to singular value decomposition (SVD). First I do not understand CD yet, since code is available I just want to try it out how it works ... • 201 1 vote 0 answers 57 views ### SVD decomposition and the update problem of matrix differential equations For a matrix Y(t) \in \mathbb{R}^{m \times n}, its rank-r approximation could be represented in a factorized SVD-like form.$$ Y(t) = U(t) S(t) V^T(t),  where $U^{T}U = I_m$, $V^{T}V = I_n$ and $S ... • 141 1 vote 0 answers 75 views ### Generate polynomial basis through a sequence of SVD I need help to understand how to use the result given by an algorithm for constructing an orthonormal polynomial basis over$L^{2}(X)$, where$X\subset\mathbb{R}^2$, with respect to the inner product$...
• 219
1 vote
54 views

I would like to calculate the Adjugate matrix of a given matrix $A$, and its updates in the diagonal: $B=A-\lambda I$, where $I$ is the identity matrix, $\lambda$ is a scalar. To this end, I am using ...
1 vote
81 views

### Stability of SVD, Eigendecompositions, and pseudoinverse procedures in modern LAPACK routines

I have proposed an optimisation algorithm which I claim has improved upon the previous algorithm in a number of ways. One of these claims is that my proposed solution requires no explicit SVD and ...
• 203
1 vote
606 views

### Pseudoinverse of a large sparse matrix in r

This question was moved from Cross-Validated: https://stats.stackexchange.com/questions/274042/pseudoinverse-of-large-sparse-matrix-in-r I am trying to calculate the pseudoinverse of a large sparse ...
• 111
92 views

### Computing smallest singular value of a matrix with explicit error control?

[Also posted here: https://mathoverflow.net/q/464433/] Many good algorithms are out there computing truncated SVD: https://mathoverflow.net/q/161252. I am trying to implement some codes to find the ...
• 161
66 views

### Formula for overdetermined logical matrix pseudoinverse not requiring SVD?

In https://commons.wikimedia.org/wiki/File:YI_%3D_PI.png, you will find a formula-based solution for an overdetermined logical matrix pseudoinverse. This simple formula gives the same result as the ...
• 101