Singular value decompositions and low rank approximations of multi-linear functionals

2007 ◽  
Author(s):  
Femke van Belzen ◽  
Siep Weiland ◽  
Jan de Graaf
Keyword(s):  
Singular Value ◽  
Low Rank ◽  
Linear Functionals ◽  
Low Rank Approximations ◽  
Singular Value Decompositions

A QUINTET SINGULAR VALUE DECOMPOSITION THROUGH EMPIRICAL MODE DECOMPOSITIONS

2014 ◽  
Vol 06 (02n03) ◽  
pp. 1450010
Author(s):  
MIN-SUNG KOH
Keyword(s):  
Singular Value Decomposition ◽  
Speech Enhancement ◽  
Singular Values ◽  
Singular Value ◽  
Diagonal Matrix ◽  
Low Rank ◽  
Orthogonal Matrices ◽  
Low Rank Approximations ◽  
Single Matrix ◽  
Value Decomposition

A particular quintet singular valued decomposition (Quintet-SVD) is introduced in this paper via empirical mode decompositions (EMDs). The Quintet-SVD results in four specific orthogonal matrices with a diagonal matrix of singular values. Furthermore, this paper shows relationships between the Quintet-SVD and traditional SVD, generalized low rank approximations of matrices (GLRAM) of one single matrix, and EMDs. One application of the Quintet-SVD for speech enhancement is shown and compared with an application of traditional SVD.

scholarly journals Principal Component Analysis and Its Derivation From Singular Value Decomposition

2019 ◽  
Vol 8 (2) ◽  
pp. 183
Author(s):  
Orumie, Ukamaka Cynthia ◽  
Ogbonna Onyinyechi
Keyword(s):  
Principal Component Analysis ◽  
Singular Value Decomposition ◽  
Principal Component ◽  
Component Analysis ◽  
Singular Value ◽  
Low Rank ◽  
Singular Value Decomposition Method ◽  
Daunting Task ◽  
Low Rank Approximations ◽  
Value Decomposition

Generally, today data analysts and researchers are often faced with a daunting task of reducing high dimensional datasets as large volume of data can be easily generated given the explosive activities of the internet. The most widely used tools for data reduction is the principal component analysis. Merely in some cases, the singular value decomposition method is applied. The study examined the application and theoretical framework of these methods in terms of its linear algebra foundation. The study discovered that the SVD method is a more robust and general method for a change of basis and low rank approximations. But.in terms of application, the PCA method is easy to interpret as illustrated in the work.

scholarly journals A parallel hierarchical blocked adaptive cross approximation algorithm

2020 ◽  
Vol 34 (4) ◽  
pp. 394-408
Author(s):  
Yang Liu ◽  
Wissam Sid-Lakhdar ◽  
Elizaveta Rebrova ◽  
Pieter Ghysels ◽  
Xiaoye Sherry Li
Keyword(s):  
Computational Complexity ◽  
Approximation Algorithm ◽  
Singular Value ◽  
Decomposition Algorithm ◽  
Low Rank ◽  
Adaptive Cross Approximation ◽  
Rank Revealing ◽  
Singular Value Decompositions ◽  
Rank Decomposition ◽  
Low Rank Decomposition

This article presents a low-rank decomposition algorithm based on subsampling of matrix entries. The proposed algorithm first computes rank-revealing decompositions of submatrices with a blocked adaptive cross approximation (BACA) algorithm, and then applies a hierarchical merge operation via truncated singular value decompositions (H-BACA). The proposed algorithm significantly improves the convergence of the baseline ACA algorithm and achieves reduced computational complexity compared to the traditional decompositions such as rank-revealing QR. Numerical results demonstrate the efficiency, accuracy, and parallel scalability of the proposed algorithm.

scholarly journals Asymptotic Behavior of Singular and Entropy Numbers for Some Riemann–Liouville Type Operators

2001 ◽  
Vol 8 (2) ◽  
pp. 323-332
Author(s):  
A. Meskhi
Keyword(s):  
Asymptotic Behavior ◽  
Integral Operators ◽  
Integral Transforms ◽  
Singular Value ◽  
Entropy Numbers ◽  
Liouville Type ◽  
Singular Value Decompositions

Abstract The asymptotic behavior of the singular and entropy numbers is established for the Erdelyi–Köber and Hadamard integral operators (see, e.g., [Samko, Kilbas and Marichev, Integrals and derivatives. Theoryand Applications, Gordon and Breach Science Publishers, 1993]) acting in weighted L 2 spaces. In some cases singular value decompositions are obtained as well for these integral transforms.

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