An alternating shifted inverse power method for the extremal eigenvalues of fourth-order partially symmetric tensors

Chunyan Wang; Haibin Chen; Yiju Wang; Hong Yan

doi:10.1016/j.aml.2023.108601

An alternating shifted inverse power method for the extremal eigenvalues of fourth-order partially symmetric tensors

Chunyan Wang, Haibin Chen^*, Yiju Wang, Hong Yan

^*Corresponding author for this work

Department of Electrical Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

4 Citations (Scopus)

Abstract

Extremal M-eigenvalues of fourth-order partially symmetric tensors play an important role in the nonlinear elastic material analysis and the entanglement problem in quantum physics. In this paper, we propose an alternating shifted inverse power method for computing the extremal M-eigenvalues of fourth-order partially symmetric tensors. The proposed algorithm is simple to operate and easy to understand for convergence analysis. Numerical experiments show the effectiveness of the proposed method. © 2023 Elsevier Ltd

Original language	English
Article number	108601
Journal	Applied Mathematics Letters
Volume	141
Online published	3 Feb 2023
DOIs	https://doi.org/10.1016/j.aml.2023.108601
Publication status	Published - Jul 2023

Funding

This work is supported by National Natural Science Foundation of China (12071249, 12071250), Shandong Provincial Natural Science Foundation of Distinguished Young Scholars, China (ZR2021JQ01), Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA) and Hong Kong Research Grants Council (Project CityU 11204821)

Research Keywords

Fourth-order partially symmetric tensor
Inverse power method
M-eigenvalues

RGC Funding Information

RGC-funded

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title = "An alternating shifted inverse power method for the extremal eigenvalues of fourth-order partially symmetric tensors",

abstract = "Extremal M-eigenvalues of fourth-order partially symmetric tensors play an important role in the nonlinear elastic material analysis and the entanglement problem in quantum physics. In this paper, we propose an alternating shifted inverse power method for computing the extremal M-eigenvalues of fourth-order partially symmetric tensors. The proposed algorithm is simple to operate and easy to understand for convergence analysis. Numerical experiments show the effectiveness of the proposed method. {\textcopyright} 2023 Elsevier Ltd",

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language = "English",

volume = "141",

journal = "Applied Mathematics Letters",

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TY - JOUR

T1 - An alternating shifted inverse power method for the extremal eigenvalues of fourth-order partially symmetric tensors

AU - Wang, Chunyan

AU - Chen, Haibin

AU - Wang, Yiju

AU - Yan, Hong

PY - 2023/7

Y1 - 2023/7

N2 - Extremal M-eigenvalues of fourth-order partially symmetric tensors play an important role in the nonlinear elastic material analysis and the entanglement problem in quantum physics. In this paper, we propose an alternating shifted inverse power method for computing the extremal M-eigenvalues of fourth-order partially symmetric tensors. The proposed algorithm is simple to operate and easy to understand for convergence analysis. Numerical experiments show the effectiveness of the proposed method. © 2023 Elsevier Ltd

AB - Extremal M-eigenvalues of fourth-order partially symmetric tensors play an important role in the nonlinear elastic material analysis and the entanglement problem in quantum physics. In this paper, we propose an alternating shifted inverse power method for computing the extremal M-eigenvalues of fourth-order partially symmetric tensors. The proposed algorithm is simple to operate and easy to understand for convergence analysis. Numerical experiments show the effectiveness of the proposed method. © 2023 Elsevier Ltd

KW - Fourth-order partially symmetric tensor

KW - Inverse power method

KW - M-eigenvalues

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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85147607882&origin=recordpage

U2 - 10.1016/j.aml.2023.108601

DO - 10.1016/j.aml.2023.108601

M3 - RGC 21 - Publication in refereed journal

SN - 0893-9659

VL - 141

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

M1 - 108601

ER -

An alternating shifted inverse power method for the extremal eigenvalues of fourth-order partially symmetric tensors

Abstract

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Research Keywords

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GRF: Matching Large Feature Sets based on Hypergraph Models and Structurally Adaptive CUR Decompositions of Compatibility Tensors

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An alternating shifted inverse power method for the extremal eigenvalues of fourth-order partially symmetric tensors

Abstract

Funding

Research Keywords

RGC Funding Information

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

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GRF: Matching Large Feature Sets based on Hypergraph Models and Structurally Adaptive CUR Decompositions of Compatibility Tensors

Cite this