{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:27:40Z","timestamp":1760171260789,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,15]],"date-time":"2022-02-15T00:00:00Z","timestamp":1644883200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The project is supported by Fujian Natural Science Foundation","award":["Grant No. 2019J01879"],"award-info":[{"award-number":["Grant No. 2019J01879"]}]},{"name":"Key Reform in Education","award":["Grant No. FBJG20200310"],"award-info":[{"award-number":["Grant No. FBJG20200310"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The tensor absolute value equation is a class of interesting structured multilinear systems. In this article, from the perspective of pure numerical algebra, we first consider a tensor-type successive over-relaxation method (SOR) (called TSOR) and tensor-type accelerated over-relaxation method (AOR) (called TAOR) for solving tensor absolute value equations. Furthermore, one type of preconditioned tensor splitting method is also applied for solving structured multilinear systems. Numerical experiments adequately demonstrate the efficiency of the presented methods.<\/jats:p>","DOI":"10.3390\/sym14020387","type":"journal-article","created":{"date-parts":[[2022,2,15]],"date-time":"2022-02-15T22:44:57Z","timestamp":1644965097000},"page":"387","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Efficient Splitting Methods for Solving Tensor Absolute Value Equation"],"prefix":"10.3390","volume":"14","author":[{"given":"Jing","family":"Ning","sequence":"first","affiliation":[{"name":"College of Computer and Information Sciences, Fujian Agriculture and Forestry University, Fuzhou 350108, China"}]},{"given":"Yajun","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Big Data, Fuzhou University of International Studies and Trade, Fuzhou 350202, China"}]},{"given":"Jie","family":"Yao","sequence":"additional","affiliation":[{"name":"School of Big Data, Fuzhou University of International Studies and Trade, Fuzhou 350202, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"e2280","DOI":"10.1002\/nla.2280","article-title":"Extrapolation methods for fixed-point multilinear PageRank computations","volume":"27","author":"Cipolla","year":"2020","journal-title":"Numer. 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