An<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si16.gif" display="inline" overflow="scroll"><mml:mi>H</mml:mi></mml:math>-tensor based iterative scheme for identifying the positive definiteness of multivariate homogeneous forms

Zhang, Kaili; Wang, Yiju

doi:10.1016/j.cam.2016.03.025

Cited by 62 publications

(23 citation statements)

References 24 publications

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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%

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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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Section: Introductionmentioning

confidence: 99%

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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“…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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“…For more information, see e.g. [6][7][8]13,18,21,23,27,30,32,33,38,40,47,50,[52][53][54][55]57,64,[69][70][71][72].Throughout this paper, we assume that the solution set of (1.1) is nonempty.…”

Section: Introductionmentioning

confidence: 99%

A linearly convergent algorithm for sparse signal reconstruction

Feng

Wang²

2018

J. Fixed Point Theory Appl.

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For the sparse signal reconstruction problem in compressive sensing, we propose a projection-type algorithm without any backtracking line search based on a new formulation of the problem. Under suitable conditions, global convergence and its linear convergence of the designed algorithm are established. The efficiency of the algorithm is illustrated through some numerical experiments on some sparse signal reconstruction problem.Mathematics Subject Classifications. 65H10, 90C33, 90C30.

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AnH-tensor based iterative scheme for identifying the positive definiteness of multivariate homogeneous forms

Cited by 62 publications

References 24 publications

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

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

A linearly convergent algorithm for sparse signal reconstruction

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