C-eigenvalue inclusion theorems for piezoelectric-type tensors

Che, Haitao; Chen, Haibin; Wang, Yiju

doi:10.1016/j.aml.2018.09.014

Cited by 28 publications

(19 citation statements)

References 22 publications

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“…In this example, we give eight piezoelectric-type tensors, from Curie and Curie (1880) Che et al (2019), , Wang et al (2020) and Theorem 7 The largest C-eigenvalue λ * of the above eight piezoelectric-type tensors and its bounds are list in Table 4, where ρ := ρ(A 1:: ), . .…”

Section: Examplementioning

confidence: 99%

“…. , ρ(A n:: ) 2 , ρ C = min{ρ , ρ L , ρ M }, and ρ, ρ C , ρ min and ρ γ are obtained respectively by Theorem 7, Theorems 2.1, 2.2 and 2.4 of Che et al (2019), Theorem 3 of and Theorem 2.1 of Wang et al (2020).…”

Section: Examplementioning

confidence: 99%

“…Recently, many researchers have also been interested in studying the C-eigenvalues of piezoelectric-type tensors (see Chen et al 2017;Che et al 2019;Wang et al 2020). The piezoelectric-type tensors introduced by Chen et al (2017) have extensive applications in physics and engineering (Curie and Curie 1880;Nye 1985).…”

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confidence: 99%

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Eigenvalue bounds of third-order tensors via the minimax eigenvalue of symmetric matrices

Chen

et al. 2020

Comp. Appl. Math.

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Upper and lower bounds for H-eigenvalues, Z-spectral radius and C-spectral radius of a thirdorder tensor are given by the minimax eigenvalue of symmetric matrices extracted from this given tensor. As applications, a sufficient condition for third-order nonsingular M-tensors and some valid sufficient conditions for the uniqueness and solvability of the solutions to multi-linear systems, tensor complementarity problems and non-homogeneous systems are proposed. Keywords H-eigenvalues • Z-eigenvalues • C-eigenvalues • Nonsingular M-tensors • Tensor complementarity problems • Piezoelectric-type tensors Mathematics Subject Classification 15A18 • 15A42 • 15A69 1 Introduction Third-order tensors have received much attention and have extensive applications in physics, engineering and scientific computing (Grozdanov and Kaplis 2016; Sørensen and De Lath-Communicated by Yimin Wei.

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Section: Examplementioning

confidence: 99%

Section: Examplementioning

confidence: 99%

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Eigenvalue bounds of third-order tensors via the minimax eigenvalue of symmetric matrices

Chen

et al. 2020

Comp. Appl. Math.

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“…which is applied to intensity-modulated radiation therapy [1][2][3][4][5][6][7][8][9][10][11], signal processing [12][13][14][15][16][17][18][19][20][21], and image reconstruction [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Censor et al [39] proposed the proximity function pðxÞ to measure the distance of a point to all sets…”

Section: Introductionmentioning

confidence: 99%

A Relaxed Self-Adaptive Projection Algorithm for Solving the Multiple-Sets Split Equality Problem

Che

Chen

2020

Journal of Function Spaces

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In this article, we introduce a relaxed self-adaptive projection algorithm for solving the multiple-sets split equality problem. Firstly, we transfer the original problem to the constrained multiple-sets split equality problem and a fixed point equation system is established. Then, we show the equivalence of the constrained multiple-sets split equality problem and the fixed point equation system. Secondly, we present a relaxed self-adaptive projection algorithm for the fixed point equation system. The advantage of the self-adaptive step size is that it could be obtained directly from the iterative procedure. Furthermore, we prove the convergence of the proposed algorithm. Finally, several numerical results are shown to confirm the feasibility and efficiency of the proposed algorithm.

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“…In this sense, A = (a ijkl ) is called a fourth-order partially symmetric tensor, denoted by A ∈ E 4,n Problem (1.1) arises from some practical problems such as nonlinear elastic materials analysis and quantum physics [17,18,23,12,20,5,6,7,25,4,9,10,28,29,32,31,26,30,3,24]. The strong ellipticity condition plays important roles in nonlinear elasticity and materials.…”

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confidence: 99%

New M-eigenvalue intervals and application to the strong ellipticity of fourth-order partially symmetric tensors

Che¹,

Chen²,

Zhou³

2021

JIMO

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M-eigenvalues of fourth-order partially symmetric tensors play an important role in nonlinear elasticity and materials. In this paper, we present some M-eigenvalue intervals to locate all M-eigenvalues of fourth-order partially symmetric tensors. It is proved that the new interval is tighter than the one proposed by He, Li and Wei [16]. Furthermore, we obtain some new checkable sufficient conditions for the strong ellipticity of fourth-order partially symmetric tensors. Three numerical examples arising from anisotropic materials are presented to verify the efficiency of the proposed results.

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C-eigenvalue inclusion theorems for piezoelectric-type tensors

Cited by 28 publications

References 22 publications

Eigenvalue bounds of third-order tensors via the minimax eigenvalue of symmetric matrices

Eigenvalue bounds of third-order tensors via the minimax eigenvalue of symmetric matrices

A Relaxed Self-Adaptive Projection Algorithm for Solving the Multiple-Sets Split Equality Problem

New M-eigenvalue intervals and application to the strong ellipticity of fourth-order partially symmetric tensors

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