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M-positive semi-definiteness and M-positive definiteness of fourth-order partially symmetric Cauchy tensors [PDF]
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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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 Criterions-Based
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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New Sufficient Condition for the Positive Definiteness of Fourth Order Tensors
Mathematics, 2018 In this paper, we give a new Z-eigenvalue localization set for Z-eigenvalues of structured fourth order tensors. As applications, a sharper upper bound for the Z-spectral radius of weakly symmetric nonnegative fourth order tensors is obtained and a new Z-
Jun He +3 more
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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 +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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Positive Inductive-Recursive Definitions [PDF]
Logical Methods in Computer Science, 2013 A new theory of data types which allows for the definition of types as initial algebras of certain functors Fam(C) -> Fam(C) is presented. This theory, which we call positive inductive-recursive definitions, is a generalisation of Dybjer and Setzer's theory of inductive-recursive definitions within which C had to be discrete -- our work can ...
Ghani, Neil +2 more
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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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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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Open Mathematics, 2021 Positive definite polynomials are important in the field of optimization. ℋ-tensors play an important role in identifing the positive definiteness of an even-order homogeneous multivariate form.
Sun Deshu, Bai Dongjian
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