Results 1 to 10 of about 1,086 (62)
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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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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On Regular Signed Graphs with Three Eigenvalues
Discussiones Mathematicae Graph Theory, 2020 In this paper our focus is on regular signed graphs with exactly 3 (distinct) eigenvalues. We establish certain basic results; for example, we show that they are walk-regular.
Anđelić Milica +2 more
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Eigenvalue inclusion sets for linear response eigenvalue problems
Demonstratio Mathematica, 2022 In this article, some inclusion sets for eigenvalues of a matrix in the linear response eigenvalue problem (LREP) are established. It is proved that the inclusion sets are tighter than the Geršgorin-type sets.
He Jun, Liu Yanmin, Lv Wei
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A modified variant of HSS preconditioner for generalized saddle point problems
Advances in Mechanical Engineering, 2022 Recently, Zhang [Numerical Linear Algebra with Applications, 2018: e2166] constructed an efficient variant of Hermitian and skew-Hermitian splitting (HSS) preconditioner for generalized saddle point problems, and gave the corresponding theoretical ...
Li-Tao Zhang, Yi-Fan Zhang
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A new generalized shift-splitting method for nonsymmetric saddle point problems
Advances in Mechanical Engineering, 2022 Recently, Huang and Huang [ Journal of Computational and Applied Mathematics , 328 (2018) 381–399] proposed a modified generalized shift-splitting preconditioned (denoted by MGSSP) method for solving large sparse saddle point problems, and gave the ...
Tao Wei, Li-Tao Zhang
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Perturbations in a Signed Graph and its Index
Discussiones Mathematicae Graph Theory, 2018 In this paper we consider the behaviour of the largest eigenvalue (also called the index) of signed graphs under small perturbations like adding a vertex, adding an edge or changing the sign of an edge.
Stanić Zoran
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Perturbed spectra of defective matrices
Journal of Applied Mathematics, Volume 2003, Issue 3, Page 115-140, 2003., 2003 This paper is devoted to the perturbation theory for defective matrices. We consider the asymptotic expansions of the perturbed spectrum when a matrix A is changed to A + tE, where E ≠ 0 and t > 0 is a small parameter. In particular, we analyse the rational exponents that may occur when the matrix E varies over the sphere ‖E‖ = ρ > 0.
Mihail Konstantinov +2 more
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Journal of Applied Mathematics, Volume 2003, Issue 9, Page 459-485, 2003., 2003 A comprehensive treatment of Rayleigh‐Schrödinger perturbation theory for the symmetric matrix eigenvalue problem is furnished with emphasis on the degenerate problem. The treatment is simply based upon the Moore‐Penrose pseudoinverse thus distinguishing it from alternative approaches in the literature.
Brian J. McCartin
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International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 6, Page 397-409, 2001., 2001 Solving systems of nonlinear equations and inequalities is of critical importance in many engineering problems. In general, the existence of inequalities in the problem adds to its difficulty. We propose a new projected Hessian Gauss‐Newton algorithm for solving general nonlinear systems of equalities and inequalities.
Mahmoud M. El-Alem +2 more
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