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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 definite measures [PDF]
Proceedings of the American Mathematical Society, 1963 In this paper we prove two theorems relating positive definite measures to induced representations. The first shows how the injection of a positive definite measure on a topological group H into a containing locally compact group G in which H is closed gives rise to induced representations.
Robert J. Blattner
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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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Positive Definiteness and Semi-Definiteness of Even Order Symmetric Cauchy Tensors [PDF]
, 2014 Motivated by symmetric Cauchy matrices, we define symmetric Cauchy tensors and their generating vectors in this paper. Hilbert tensors are symmetric Cauchy tensors.
Haibin Chen, L. Qi
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Complexity, 2020 M-eigenvalues of fourth-order partially symmetric tensors play important roles in the nonlinear elastic material analysis and the entanglement problem of quantum physics.
Gang Wang, Linxuan Sun, Lixia Liu
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Products of positive definite matrices. I [PDF]
Pacific Journal of Mathematics, 1967 I. The author gives, for every positive integer \(j\), necessary and sufficient conditions for a \(2\times 2\) real matrix (with positive determinant) to be a product of \(j\) positive definite real symmetric matrices (if \(j\ge 5\), every real matrix with positive determinant can be written as such a product).
C.S. Ballantine
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Transporting positive definiteness
Acta Scientiarum Mathematicarum, 2022 This is a rough guide to the topic which might be worthy to develop further on. Expanding positive definiteness beyond its presupposed scope is intriguing due to a number of possible applications. The paper though looking at the first glance a little bit
F. H. Szafraniec
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Positive Definiteness of the Blended Force-Based Quasicontinuum Method [PDF]
Multiscale Modeling & simulation, 2011 The development of consistent and stable quasicontinuum models for multidimensional crystalline solids remains a challenge. For example, proving the stability of the force-based quasicontinuum (QCF) model [M. Dobson and M. Luskin, M2AN Math. Model. Numer.
X. Li, M. Luskin, C. Ortner
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On Dugundji’s notion of positive definiteness [PDF]
Proceedings of the American Mathematical Society, 1974 Dugundji’s notion of positive definiteness is generalized to nonnegative real-valued functions on a uniform space. Its relations with completeness and various notions of compactness are investigated. For an arbitrary uniform space X X , there may be lack of the right kind of lower semicontinuous real-valued functions on X ...
Chi Song Wong
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Positive Definiteness via Off-Diagonal Scaling of a Symmetric Indefinite Matrix. [PDF]
Psychometrika, 2011 Bentler PM, Yuan KH.
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