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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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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
3 votes
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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 ...
olamundo's user avatar
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2 votes
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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 ...
5d41402abc4's user avatar
2 votes
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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 ...
mana's user avatar
  • 131
2 votes
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758 views

finding null space to a complex matrix

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 &\...
Physicist's user avatar
  • 217
2 votes
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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 ...
Justin Solomon's user avatar
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 ...
sv_jan5's user avatar
  • 121
2 votes
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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 ...
hertzsprung's user avatar
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 ...
Parag's user avatar
  • 201
1 vote
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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 ...
Owen Jun's user avatar
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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 $...
Raibyo's user avatar
  • 219
1 vote
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updating the matrix Adjugate/Cofactor

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 ...
user2393987's user avatar
1 vote
0 answers
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 ...
tisPrimeTime's user avatar
1 vote
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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 ...
Paul's user avatar
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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 ...
Ma Joad's user avatar
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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 ...
Youvan's user avatar
  • 101
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342 views

Explanation of Givens rotation in Jacobi Rotation SVD

I'm trying to implement Singular Value Decomposition (homework of sorts) via the Jacobi Rotation method (more info here, pages 11 and 12). I am stuck at the bullet saying (sorry for the picture, but I'...
cyau's user avatar
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