Criteria for strong H-tensors

Wang, Yiju; Zhang, Kaili; Sun, Huaijiang

doi:10.1007/s11464-016-0525-z

Cited by 51 publications

(31 citation statements)

References 26 publications

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“…where the operation ‖ ⋅ ‖ is defined by (13). From Table 1, it is observed that the estimates from TPTA can reach the desired accuracy.…”

Section: Application For Computing the Tensor Exponential Functionmentioning

confidence: 96%

“…Recently, tensor computation, especially eigenvalues of tensors, has attracted attention of many scholars; some important results have been found in the current literature [8][9][10][11][12][13][14][15]. For instance, computation of exp(A ) is required in applications such as finite strain hyperelasticbased multiplicative plasticity models [7,[16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

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The Tensor Pade´-Type Approximant with Application in Computing Tensor Exponential Function

Liu

2018

Journal of Function Spaces

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Tensor exponential function is an important function that is widely used. In this paper, tensor Pad-type approximant (TPTA) is defined by introducing a generalized linear functional for the first time. The expression of TPTA is provided with the generating function form. Moreover, by means of formal orthogonal polynomials, we propose an efficient algorithm for computing TPTA. As an application, the TPTA for computing the tensor exponential function is presented. Numerical examples are given to demonstrate the efficiency of the proposed algorithm.

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“…where the operation ‖ ⋅ ‖ is defined by (13). From Table 1, it is observed that the estimates from TPTA can reach the desired accuracy.…”

Section: Application For Computing the Tensor Exponential Functionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

The Tensor Pade´-Type Approximant with Application in Computing Tensor Exponential Function

Liu

2018

Journal of Function Spaces

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“…As the extension of matrix computation, tensor computation is the latest research hotspot in the last twenty years . In particular, various kinds of tensor equations arise from mechanics, physics, Markov process, control theory, partial differential equations, and engineering problems .…”

Section: Introductionmentioning

confidence: 99%

“…As the extension of matrix computation, tensor computation is the latest research hotspot in the last twenty years. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] In particular, various kinds of tensor equations arise from mechanics, physics, Markov process, control theory, partial differential equations, and engineering problems. [18][19][20][21][22] The radiation transfer equation, the high-dimensional Poisson equation, the Einstein gravitational field equation, and the piezoelectric effect equation are all tensor equations.…”

Section: Introductionmentioning

confidence: 99%

Krylov subspace methods to solve a class of tensor equations via the Einstein product

Huang

Xie

2019

Numerical Linear Algebra App

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Summary This paper is concerned with some of the well‐known iterative methods in their tensor forms to solve a class of tensor equations via the Einstein product. More precisely, the tensor forms of the Arnoldi and Lanczos processes are derived and the tensor form of the global GMRES method is presented. Meanwhile, the tensor forms of the MINIRES and SYMMLQ methods are also established. The proposed methods use tensor computations with no matricizations involved. Numerical examples are provided to illustrate the efficiency of the proposed methods and testify the conclusions suggested in this paper.

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“…The problem finds applications in fields such as economics, mathematical programming, transportation, and regional science [1][2][3][4][5], and it has received much attention from researchers; see, e.g., [6][7][8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

An Objective Penalty Function-Based Method for Inequality Constrained Minimization Problem

Lian

Meng

Wang

2018

Mathematical Problems in Engineering

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For inequality constrained minimization problem, we first propose a new exact nonsmooth objective penalty function and then apply a smooth technique to the penalty function to make it smooth. It is shown that any minimizer of the smoothing objective penalty function is an approximated solution of the original problem. Based on this, we develop a solution method for the inequality constrained minimization problem and prove its global convergence. Numerical experiments are provided to show the efficiency of the proposed method.

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Criteria for strong H-tensors

Cited by 51 publications

References 26 publications

The Tensor Pade´-Type Approximant with Application in Computing Tensor Exponential Function

The Tensor Pade´-Type Approximant with Application in Computing Tensor Exponential Function

Krylov subspace methods to solve a class of tensor equations via the Einstein product

An Objective Penalty Function-Based Method for Inequality Constrained Minimization Problem

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