Notes and counterexamples on positive (semi) definite properties of some matrix products
Ain Shams Engineering Journal, 2018 In the present paper, we give some notes and counterexamples to show that the positive (semi) definite property of the Khatri-Rao and Tracy-Singh products of partitioned matrices are in general incorrect and show also that the matrix triangle inequality ...
Zeyad Al-Zhour
doaj +2 more sources
Fast evaluation of nonlinear functionals of tensor product wavelet expansions [PDF]
, 2010 For a nonlinear functional f, and a function u from the span of a set of tensor product interpolets, it is shown how to compute the interpolant of f (u) from the span of this set of tensor product interpolets in linear complexity, assuming that the index
Christoph Schwab +5 more
core +2 more sources
A concise proof to the spectral and nuclear norm bounds through tensor partitions
Open Mathematics, 2019 On estimations of the lower and upper bounds for the spectral and nuclear norm of a tensor, Li established neat bounds for the two norms based on regular tensor partitions, and proposed a conjecture for the same bounds to be hold based on general tensor ...
Kong Xu
doaj +1 more source
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
doaj +1 more source
Two new eigenvalue localization sets for tensors and theirs applications
Open Mathematics, 2017 A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Qi (J. Symbolic Comput., 2005, 40, 1302-1324) and Li et al. (Numer. Linear Algebra Appl., 2014, 21, 39-50).
Zhao Jianxing, Sang Caili
doaj +1 more source
Some inequalities on the spectral radius of nonnegative tensors
Open Mathematics, 2020 The eigenvalues and the spectral radius of nonnegative tensors have been extensively studied in recent years. In this paper, we investigate the analytic properties of nonnegative tensors and give some inequalities on the spectral radius.
Ma Chao +3 more
doaj +1 more source
Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints
, 2010 Bi-quadratic optimization, Semidefinite programming relaxation, Approximation solution, Probabilistic solution, 15A69, 90C22, 90C26, 90C59,
Liqun Qi +5 more
core +1 more source
An S-type upper bound for the largest singular value of nonnegative rectangular tensors
Open Mathematics, 2016 An S-type upper bound for the largest singular value of a nonnegative rectangular tensor is given by breaking N = {1, 2, … n} into disjoint subsets S and its complement. It is shown that the new upper bound is smaller than that provided by Yang and Yang (
Zhao Jianxing, Sang Caili
doaj +1 more source
New bounds for the minimum eigenvalue of 𝓜-tensors
Open Mathematics, 2017 A new lower bound and a new upper bound for the minimum eigenvalue of an 𝓜-tensor are obtained. It is proved that the new lower and upper bounds improve the corresponding bounds provided by He and Huang (J. Inequal.
Zhao Jianxing, Sang Caili
doaj +1 more source
Characterization generalized derivations of tensor products of nonassociative algebras
Demonstratio MathematicaConsider A{\mathcal{A}} and ℬ{\mathcal{ {\mathcal B} }} to be nonassociative unital algebras. Under the assumption that either one of them has finite dimensions or that both are finite dimensions, a generalized derivation is an additive map ℱ:A→A ...
Aboubakr Ahmed
doaj +1 more source