Conditions for strong ellipticity and M-eigenvalues
From MaRDI portal
Publication:1042549
DOI10.1007/s11464-009-0016-6zbMath1233.74004OpenAlexW1976492279MaRDI QIDQ1042549
Deren Han, Hui-Hui Dai, Liqun Qi
Publication date: 14 December 2009
Published in: Frontiers of Mathematics in China (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11464-009-0016-6
Related Items (60)
Bounds of M-eigenvalues and strong ellipticity conditions for elasticity tensors ⋮ Localization and calculation for C-eigenvalues of a piezoelectric-type tensor ⋮ Sharp upper bounds on the maximum \(M\)-eigenvalue of fourth-order partially symmetric nonnegative tensors ⋮ Rank-1 Tensor Properties with Applications to a Class of Tensor Optimization Problems ⋮ Criteria for the strong ellipticity condition of a partially symmetric tensor ⋮ The dominant eigenvalue of an essentially nonnegative tensor ⋮ Structured multi-way arrays and their applications ⋮ New M-eigenvalue intervals and application to the strong ellipticity of fourth-order partially symmetric tensors ⋮ Convergence of an algorithm for the largest singular value of a nonnegative rectangular tensor ⋮ M-eigenvalue intervals and checkable sufficient conditions for the strong ellipticity ⋮ On solving biquadratic optimization via semidefinite relaxation ⋮ Conditions of strong ellipticity and calculations of M-eigenvalues for a partially symmetric tensor ⋮ \(l^{p/2,q/2}\)-singular values of a real partially symmetric rectangular tensor ⋮ M-eigenvalue inclusion intervals for a fourth-order partially symmetric tensor ⋮ Unnamed Item ⋮ Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints ⋮ \(l^{p, q/2}\)-singular values of a real partially symmetric rectangular tensor ⋮ Shifted inverse power method for computing the smallest M-eigenvalue of a fourth-order partially symmetric tensor ⋮ Checkable criteria for the M-positive definiteness of fourth-order partially symmetric tensors ⋮ An alternating shifted inverse power method for the extremal eigenvalues of fourth-order partially symmetric tensors ⋮ A direct method for calculating M-eigenvalues of an elasticity tensor ⋮ Positive definiteness of fourth-order partially symmetric tensors ⋮ Linear convergence of an algorithm for largest singular value of a nonnegative rectangular tensor ⋮ Standard bi-quadratic optimization problems and unconstrained polynomial reformulations ⋮ Parameterized S-type M-eigenvalue inclusion intervals for fourth-order partially symmetric tensors and its applications ⋮ Bound estimations of bi-block \(M\)-eigenvalues for bi-block symmetric tensors ⋮ The partially symmetric rank-1 approximation of fourth-order partially symmetric tensors ⋮ Bounds of the minimum \(H^+\)-singular value and testing the copositiveness for rectangular tensors ⋮ Deterministic approximation algorithms for sphere constrained homogeneous polynomial optimization problems ⋮ Alternating direction method for bi-quadratic programming ⋮ Properties and methods for finding the best rank-one approximation to higher-order tensors ⋮ Approximation bounds for trilinear and biquadratic optimization problems over nonconvex constraints ⋮ New M-eigenvalue inclusion sets for fourth-order partially symmetric tensors with applications ⋮ Upper bounds for eigenvalues of Cauchy-Hankel tensors ⋮ Positive definiteness of paired symmetric tensors and elasticity tensors ⋮ New S-type inclusion theorems for the M-eigenvalues of a 4th-order partially symmetric tensor with applications ⋮ Programmable sufficient conditions for the strong ellipticity of partially symmetric tensors ⋮ Bounds for the M-spectral radius of a fourth-order partially symmetric tensor ⋮ Some inequalities for the minimum M-eigenvalue of elasticity M-tensors ⋮ Spectral properties of odd-bipartite \(Z\)-tensors and their absolute tensors ⋮ \(l^{k,s}\)-singular values and spectral radius of partially symmetric rectangular tensors ⋮ Upper bounds for the spectral radii of nonnegative tensors ⋮ Singular values of a real rectangular tensor ⋮ Standard tensor and its applications in problem of singular values of tensors ⋮ A successive approximation method for quantum separability ⋮ \(M\)-eigenvalues-based sufficient conditions for the positive definiteness of fourth-order partially symmetric tensors ⋮ Bi-block positive semidefiniteness of bi-block symmetric tensors ⋮ Biquadratic tensors, biquadratic decompositions, and norms of biquadratic tensors ⋮ Elasticity \(\mathcal{M} \)-tensors and the strong ellipticity condition ⋮ Positive Maps and Separable Matrices ⋮ On copositiveness identification of partially symmetric rectangular tensors ⋮ Partially symmetric nonnegative rectangular tensors and copositive rectangular tensors ⋮ M-positive semi-definiteness and M-positive definiteness of fourth-order partially symmetric Cauchy tensors ⋮ Spectral norm and nuclear norm of a third order tensor ⋮ Exclusion sets in eigenvalue localization sets for tensors ⋮ Sharp bounds on the minimum \(M\)-eigenvalue and strong ellipticity condition of elasticity \(Z\)-tensors-tensors ⋮ Direct methods to compute all \(Z\)-eigenpairs of a tensor with dimension 2 or 3 ⋮ Multilinear Control Systems Theory ⋮ On the M-eigenvalue estimation of fourth-order partially symmetric tensors ⋮ Z-eigenvalue intervals of even-order tensors with application to judge the strong ellipticity of an elasticity tensor
Cites Work
- Unnamed Item
- On copositive matrices and strong ellipticity for isotropic elastic materials
- Ellipticity and deformations with discontinuous gradients in finite elastostatics
- Eigenvalues and invariants of tensors
- Perron-Frobenius theorem for nonnegative tensors
- D-eigenvalues of diffusion kurtosis tensors
- Spectral decomposition of a 4th-order covariance tensor: applications to diffusion tensor MRI
- The degree of the E-characteristic polynomial of an even order tensor
- Z-eigenvalue methods for a global polynomial optimization problem
- On the ellipticity of the equations of nonlinear elastostatics for a special material
- On the failure of ellipticity of the equations for finite elastostatic plane strain
- A reformulation of the strong ellipticity conditions for unconstrained hyperelastic media
- Semidefinite programming relaxations for semialgebraic problems
- Eigenvalues of a real supersymmetric tensor
- Rank and eigenvalues of a supersymmetric tensor, the multivariate homogeneous polynomial and the algebraic hypersurface it defines
- Numerical multilinear algebra and its applications
- On eigenvalue problems of real symmetric tensors
- Global Optimization with Polynomials and the Problem of Moments
- Rank-One Approximation to High Order Tensors
- On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors
- A practical method for computing the largestM-eigenvalue of a fourth-order partially symmetric tensor
- On the Best Rank-1 and Rank-(R1 ,R2 ,. . .,RN) Approximation of Higher-Order Tensors
This page was built for publication: Conditions for strong ellipticity and M-eigenvalues