2020
DOI: 10.1002/nla.2284
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A locally and cubically convergent algorithm for computing š’µā€eigenpairs of symmetric tensors

Abstract: This paper is concerned with computing ī‰†-eigenpairs of symmetric tensors.We first show that computing ī‰†-eigenpairs of a symmetric tensor is equivalent to finding the nonzero solutions of a nonlinear system of equations, and then propose a modified normalized Newton method (MNNM) for it. Our proposed MNNM method is proved to be locally and cubically convergent under some suitable conditions, which greatly improves the Newton correction method and the orthogonal Newton correction method recently provided by Jaff… Show more

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Cited by 9 publications
(15 citation statements)
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“…For RGNN model, computing ī‰†-eigenpairs of a tensor is equivalent to finding the nonzero solutions of a nonlinear system of equations. 1 Finally, numerical experiments are given to show that RGNN has efficient computation for some large-scale tensors besides computing all the ī‰†-eigenpairs of small-scale general tensors. Whereas, how to choose a suitable parameter still remains an open problem.…”
Section: Discussionmentioning
confidence: 99%
See 3 more Smart Citations
“…For RGNN model, computing ī‰†-eigenpairs of a tensor is equivalent to finding the nonzero solutions of a nonlinear system of equations. 1 Finally, numerical experiments are given to show that RGNN has efficient computation for some large-scale tensors besides computing all the ī‰†-eigenpairs of small-scale general tensors. Whereas, how to choose a suitable parameter still remains an open problem.…”
Section: Discussionmentioning
confidence: 99%
“…In recent years, there has been tremendous interest in computing š’µā€eigenpairs of tensors defined as follows: 1 Let š’œāˆˆā„[m,n] be an m thā€order n ā€dimensional tensor. The goal is to find a real vectorā€scalar pair (x,Ī») with xā‰ 0 satisfying š’œxmāˆ’1=Ī»xandxTx=1, where š’œxmāˆ’1 is a vector in ā„n with (š’œxmāˆ’1)i=āˆ‘i2=1nā‹Æāˆ‘im=1naii2ā€¦imxi2ā‹Æxim,i=1,2,ā€¦,n.…”
Section: Introductionmentioning
confidence: 99%
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“…To address this issue, Kolda and Mayo in [11] further added an adaptive procedure for choosing the shift. Most recently, Zhao et al [20] proposed a modified normalized Newton method (MNNM) for computing Z-eigenpairs of symmetric tensors which can be convergent cubically. For the nonnegative tensors, Guo et al [7] proposed a modified Newton iteration (MNI) to find some positive Z-eigenpairs and showed that their method has a local quadratic convergence under appropriate assumptions.…”
Section: Introductionmentioning
confidence: 99%