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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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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
  • 599
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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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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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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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
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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
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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
  • 141
1 vote
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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
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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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Pseudoinverse of a large sparse matrix in r

This question was moved from Cross-Validated: I am trying to calculate the pseudoinverse of a large sparse ...
Paul's user avatar
  • 111
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Computing smallest singular value of a matrix with explicit error control?

[Also posted here:] Many good algorithms are out there computing truncated SVD: I am trying to implement some codes to find the ...
Ma Joad's user avatar
  • 161
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Formula for overdetermined logical matrix pseudoinverse not requiring SVD?

In, 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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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
  • 101