scholarly journals Regularization properties of LSQR for linear discrete ill-posed problems in the multiple singular value case and best, near best and general low rank approximations

2020 ◽  
Vol 36 (8) ◽  
pp. 085009
Author(s):  
Zhongxiao Jia
Keyword(s):  
Singular Value ◽  
Low Rank ◽  
Low Rank Approximations ◽  
Ill Posed

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.

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