Results 231 to 240 of about 6,697,803 (274)
A Multilinear Singular Value Decomposition [PDF]
SIAM Journal on Matrix Analysis and Applications, 2000 This paper investigates higher order singular value decompositions (HOSVD) as multilinear generalization of singular value decomposition (SVD), in terms of higher order tensors exhibiting symmetries as motivated by applications in higher order statistics. This includes matrix representation of higher order tensors, their rank properties, generalization
Lieven De Lathauwer, Joos Vandewalle
exaly +6 more sources
On the Early History of the Singular Value Decomposition [PDF]
SIAM Review, 1993 The singular value decomposition is the factorization of a matrix \(A\) into the product \(U \sum V^ H\), where \(U\) is a unitary matrix, \(\sum\) a diagonal matrix, and \(V^ H\) another unitary matrix. The author surveys contributions of five mathematicians -- Eugenio Beltrami (1835-1899), Camille Jordan (1838-1921), James Joseph Sylvester (1814-1897)
G W Stewart
exaly +2 more sources
Some of the next articles are maybe not open access.
Downdating the Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications, 1995Let \(A\) be a matrix with known singular values and left and/or right singular vectors, and let \(A'\) be the matrix obtained by deleting a row from \(A\). Computing the singular value decomposition (SVD) of \(A'\) from the SVD of \(A\) is called the downdating singular value decomposition problem (DSVDP).
Ming Gu 0002, Stanley C. Eisenstat
openaire +1 more source
Generalizations of the Singular Value and QR-Decompositions
SIAM Journal on Matrix Analysis and Applications, 1992The authors present multimatrix generalizations of some well-known orthogonal rank factorizations and show how the idea of a QR- decomposition (QRD), a URV- decomposition (URVD), and a singular value decomposition (SVD), which has become an important tool in the analysis and numerical solution of numerous problems, especially since the development of ...
Bart De Moor, Paul Van Dooren
exaly +4 more sources
Computing the Generalized Singular Value Decomposition
SIAM Journal of Scientific Computing, 1993Two new elements are added to \textit{C. C. Paige's} algorithm [SIAM J. Sci. Stat. Comput. 7, 1126-1146 (1986; Zbl 0621.65030)]. A new preprocessing step is introduced which reduces both matrices to upper triangular form satisfying certain rank conditions, and a new \(2\times 2\) triangular generalized singular value decomposition algorithm is ...
James Demmel
exaly +4 more sources
Continuation of Singular Value Decompositions
Mediterranean Journal of Mathematics, 2005In this work we consider computing a smooth path for a (block) singular value decomposition of a full rank matrix valued function. We give new theoretical results and then introduce and implement several algorithms to compute a smooth path. We illustrate performance of the algorithms with a few numerical examples.
L. DIECI L +2 more
openaire +1 more source
The hyperbolic singular value decomposition and applications
Proceedings of the 32nd Midwest Symposium on Circuits and Systems, 1990A new generalization of singular value decomposition (SVD), the hyperbolic SVD, is advanced, and its existence is established under mild restrictions. Two algorithms for effecting this decomposition are discussed. The new decomposition has applications in downdating in problems where the solution depends on the eigenstructure of the normal equations ...
Ruth Onn +2 more
openaire +2 more sources
Generalizing the Singular Value Decomposition
SIAM Journal on Numerical Analysis, 1976Two generalizations of the singular value decomposition are given. These generalizations provided a unified way of regarding certain matrix problems and the numerical techniques which are used to s...
openaire +2 more sources
The QLP Approximation to the Singular Value Decomposition
SIAM Journal on Scientific Computing, 1999A new decomposition, termed the pivoted QLP-decomposition, of a matrix is introduced. It is a postprocessing step to the pivoted QR-decomposition, used to determine the rank of a matrix. It is simply a further pivoted QR-decomposition of \(R^T\) of the first decomposition.
openaire +2 more sources
Functional Tensor Singular Value Decomposition
SIAM Journal on Scientific ComputingzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chuan Wang 0001 +4 more
openaire +3 more sources