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The General Linear Model and the Generalized Singular Value Decomposition [PDF]
, 2009 The general linear model with correlated error variables can be transformed by means of the generalized singular value decomposition to a very simple model (canonical form) where the least squares solution is obvious.
Knüsel, Leo
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Perturbation bounds for eigenvalues of diagonalizable matrices and singular values
Journal of Inequalities and Applications, 2016 Perturbation bounds for eigenvalues of diagonalizable matrices are derived. Perturbation bounds for singular values of arbitrary matrices are also given. We generalize some existing results.
Duanmei Zhou +3 more
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Privacy-Preserving Federated Singular Value Decomposition
Applied Sciences, 2023 Singular value decomposition (SVD) is a fundamental technique widely used in various applications, such as recommendation systems and principal component analyses.
Bowen Liu, Balázs Pejó, Qiang Tang
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The General Linear Model and the Generalized Singular Value Decomposition; Some Examples [PDF]
, 2009 The general linear model with correlated error variables can be transformed by means of the generalized singular value decomposition to a very simple model (canonical form) where the least squares solution is obvious.
Knüsel, Leo
core +1 more source
Singularity, Wielandt’s lemma and singular values
Journal of Computational and Applied Mathematics, 2010 The authors obtain some upper and lower bounds for the largest and the smallest singular values of certain complex matrices based on the entries and diagonal dominance. A relationship between largest singular value of a block matrix and its block norm matrix is obtained. Numerical examples are given to demonstrate the usefulness of their results.
Hou-Biao Li +3 more
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IEEE Open Journal of the Industrial Electronics Society, 2021 Voltage-source rectifiers (VSRs) have been widely used in modern power grids. The inductive grid impedance of the power grid poses a serious threat to the stability of the VSR.
Kai Wang +3 more
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The singular values of the GOE
Random Matrices: Theory and Applications, 2015 As a unifying framework for examining several properties that nominally involve eigenvalues, we present a particular structure of the singular values of the Gaussian orthogonal ensemble (GOE): the even-location singular values are distributed as the positive eigenvalues of a Gaussian ensemble with chiral unitary symmetry, while the odd-location ...
Bornemann, Folkmar, La Croix, Michael
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Bound for the largest singular value of nonnegative rectangular tensors
Open Mathematics, 2016 In this paper, we give a new bound for the largest singular value of nonnegative rectangular tensors when m = n, which is tighter than the bound provided by Yang and Yang in “Singular values of nonnegative rectangular tensors”, Front. Math.
He Jun +4 more
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An S-type singular value inclusion set for rectangular tensors
Journal of Inequalities and Applications, 2017 An S-type singular value inclusion set for rectangular tensors is given. Based on the set, new upper and lower bounds for the largest singular value of nonnegative rectangular tensors are obtained and proved to be sharper than some existing results ...
Caili Sang
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Determinantal inequalities of Hua-Marcus-Zhang type for quaternion matrices
Open Mathematics, 2021 In this paper, the authors extend determinantal inequalities of the Hua-Marcus-Zhang type for positive definite matrices to the corresponding ones for quaternion matrices.
Hong Yan, Qi Feng
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