Results 61 to 70 of about 5,012,670 (186)

Perturbation of Higher-Order Singular Values [PDF]

SIAM Journal on Applied Algebra and Geometry, 2017
Summary: The higher-order singular values for a tensor of order \(d\) are defined as the singular values of the \(d\) different matricizations associated with the multilinear rank. When \(d \geq 3\), the singular values are generally different for different matricizations but not completely independent.
Wolfgang Hackbusch, Daniel Kressner, André Uschmajew   +2 more
openaire   +4 more sources

Laplacian Singular Values [PDF]

Atlantis Studies in Uncertainty Modelling, 2021
Jirí Janecek, Irina Perfilieva
openaire   +2 more sources

A quadratically convergent algorithm for inverse singular value problems with multiple singular values

Results in Applied Mathematics
In 2021, for inverse singular value problems, a quadratically convergent algorithm (Wei and Chen, 2021) based on matrix multiplication (Ogita and Aishima, 2020) was designed for inverse singular value problems. Although this method has some good features
Wei Ma, Yuqing Zhu
doaj   +1 more source

Combinatorial Designs with Two Singular Values I. Uniform Multiplicative Designs [PDF]

In this and a sequel paper [10] we study combinatorial designs whose incidence matrix has two distinct singular values.These generalize 2-(v, k, É) designs, and include partial geometric designs and uniform multiplicative designs.Here we study the latter,
Spence, E., Dam, E.R. van
core  

V-singular values of rectangular tensors and their applications

Journal of Inequalities and Applications, 2019
The positive definiteness of rectangular tensors has wide applications in solid mechanics and quantum physics. By modifying the existing definition of singular value for rectangular tensors, some V-singular value inclusion sets for rectangular tensors ...
Jun He, Yanmin Liu, Guangjun Xu, Gang Liu   +3 more
doaj   +1 more source

Singular Spectrum Analysis: Methodology and Comparison [PDF]

In recent years Singular Spectrum Analysis (SSA), used as a powerful technique in time series analysis, has been developed and applied to many practical problems. In this paper, the performance of the SSA technique has been considered by applying it to a
Hassani, Hossein
core  

Rank-one perturbation bounds for singular values of arbitrary matrices

Journal of Inequalities and Applications, 2019
Rank-one perturbation of arbitrary matrices has many practical applications. In this paper, based on the relationship between the singular values and the eigenvalues, we discuss singular value variations and present two-side bounds of the singular values
Lei Zhu, Xiaofei Peng, Hao Liu
doaj   +1 more source

The singular values of \(A+B\) and \(A+iB\)

Linear Algebra and its Applications, 2009
Suppose that \(A\) and \(B\) are Hermitian square matrices. The authors establish some majorisation relations between the singular values of \(A + B\) and those of \(A + iB\), which can regarded as the matrix versions of the inequality \(|a+b| \leq \sqrt{2}\,|a+ib|\) (\(a,b \in \mathbb{R}\)). They prove that \(|||A + B||| \leq \sqrt{2}\,|||A + iB|||\),
Bhatia, Rajendra, Kittaneh, Fuad
openaire   +2 more sources

Research on rolling bearing fault diagnosis technology based on singular value decomposition

AIP Advances
To solve the difficulty of selecting the number of effective singular values in Singular Value Decomposition denoising, a new method to determine the number of effective singular values is proposed.
Jingfang Ji, Jingmin Ge
doaj   +1 more source

Componentwise Perturbation Analysis of the Singular Value Decomposition of a Matrix

Applied Sciences
A rigorous perturbation analysis is presented for the singular value decomposition (SVD) of a real matrix with full column rank. It is proved that the SVD perturbation problem is well posed only when the singular values are distinct.
Vera Angelova, Petko Petkov
doaj   +1 more source