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In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix into a rotation, followed by a rescaling followed by another rotation. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any m × n {\displaystyle m\times n} matrix.
In linear algebra, the generalized singular value decomposition (GSVD) is the name of two different techniques based on the singular value decomposition (SVD).The two versions differ because one version decomposes two matrices (somewhat like the higher-order or tensor SVD) and the other version uses a set of constraints imposed on the left and right singular vectors of a single-matrix SVD.
aaa is a one- to three-letter code describing the actual algorithm implemented in the subroutine, e.g. SV denotes a subroutine to solve linear system, while R denotes a rank-1 update. For example, the subroutine to solve a linear system with a general (non-structured) matrix using real double-precision arithmetic is called DGESV . [ 2 ] : "
In multilinear algebra, the higher-order singular value decomposition (HOSVD) of a tensor is a specific orthogonal Tucker decomposition. It may be regarded as one type of generalization of the matrix singular value decomposition. It has applications in computer vision, computer graphics, machine learning, scientific computing, and signal ...
In applied mathematics, k-SVD is a dictionary learning algorithm for creating a dictionary for sparse representations, via a singular value decomposition approach. k-SVD is a generalization of the k-means clustering method, and it works by iteratively alternating between sparse coding the input data based on the current dictionary, and updating the atoms in the dictionary to better fit the data.
A number of solutions to the problem have appeared in literature, notably Davenport's q-method, [2] QUEST and methods based on the singular value decomposition (SVD). Several methods for solving Wahba's problem are discussed by Markley and Mortari.
Tensor-CURT decomposition [6] is a generalization of matrix-CUR decomposition. Formally, a CURT tensor approximation of a tensor A is three matrices and a (core-)tensor C, R, T and U such that C is made from columns of A, R is made from rows of A, T is made from tubes of A and that the product U(C,R,T) (where the ,,-th entry of it is ′, ′, ′ ′, ′, ′, ′, ′, ′) closely ...
The origins of SSA and, more generally, of subspace-based methods for signal processing, go back to the eighteenth century (Prony's method).A key development was the formulation of the spectral decomposition of the covariance operator of stochastic processes by Kari Karhunen and Michel Loève in the late 1940s (Loève, 1945; Karhunen, 1947).