Results 1 to 10 of about 6,786 (248)

An ℋ-tensor-based criteria for testing the positive definiteness of multivariate homogeneous forms

Open Mathematics, 2022
A positive definite homogeneous multivariate form plays an important role in the field of optimization, and positive definiteness of the form can be identified by a special structured tensor.
Bai Dongjian, Wang Feng
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New methods based H-tensors for identifying the positive definiteness of multivariate homogeneous forms

AIMS Mathematics, 2021
Positive definite polynomials are important in the field of optimization. H-tensors play an important role in identifying the positive definiteness of an even-order homogeneous multivariate form.
Dongjian Bai, Feng Wang
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Some new criteria for judging H-tensors and their applications

AIMS Mathematics, 2023
H-tensors play a key role in identifying the positive definiteness of even-order real symmetric tensors. Some criteria have been given since it is difficult to judge whether a given tensor is an H-tensor, and their range of judgment has been limited.
Wenbin Gong, Yaqiang Wang
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Positive Definiteness of Symmetric Rank 1 (H-Version) Update for Unconstrained Optimization

مجلة بغداد للعلوم, 2022
Several attempts have been made to modify the quasi-Newton condition in order to obtain rapid convergence with complete properties (symmetric and positive definite) of the inverse of  Hessian matrix (second derivative of the objective function).
Saad Shakir Mahmood, Jaafer Hmood Eidi, Jinan Adel Jasem   +2 more
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Positive definiteness: from scalar to operator-valued kernels [PDF]

Surveys in Mathematics and its Applications, 2021
In this paper we present a short overview of results that provide relationships among scalar, matrix-valued and certain operator-valued positive definite kernels.
V. A. Menegatto
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New Criterions-Based $\mathcal{H}$-Tensors for Testing the Positive Definiteness of Multivariate Homogeneous Forms

Mathematics, 2022
Positive definite homogeneous multivariate forms play an important role in polynomial problems and medical imaging, and the definiteness of forms can be tested using structured tensors.
Dongjian Bai, Feng Wang
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On a Class of Positive Definite Operators and Their Application in Fractional Calculus

Axioms, 2022
This paper is devoted to the spectral analysis of one class of integral operators, associated with the boundary value problems for differential equations of fractional order. Approximation matrices are also investigated.
Temirkhan Aleroev
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M-positive semi-definiteness and M-positive definiteness of fourth-order partially symmetric Cauchy tensors

Journal of Inequalities and Applications, 2019
Inspired by symmetric Cauchy tensors, we define fourth-order partially symmetric Cauchy tensors with their generating vectors. In this article, we focus on the necessary and sufficient conditions for the M-positive semi-definiteness and M-positive ...
Haitao Che, Haibin Chen, Yiju Wang
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On Positive Definite Kernels of Integral Operators Corresponding to the Boundary Value Problems for Fractional Differential Equations

Entropy, 2022
In the spectral analysis of operators associated with Sturm–Liouville-type boundary value problems for fractional differential equations, the problem of positive definiteness or the problem of Hermitian nonnegativity of the corresponding kernels plays an
Mukhamed Aleroev, Temirkhan Aleroev
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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
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