乐胖代购免代理版

{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T11:07:45Z","timestamp":1726052865756},"reference-count":35,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2021,2,14]],"date-time":"2021-02-14T00:00:00Z","timestamp":1613260800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11761024,11561015,11961012"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004607","name":"Natural Science Foundation of Guangxi Province","doi-asserted-by":"publisher","award":["2016GXNSFAA380074, 2016GXNSFFA380009, 2017GXNSFBA1"],"id":[{"id":"10.13039\/501100004607","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[2021,8]]},"abstract":"Abstract<\/jats:title>The l<\/jats:italic> parameterized generalized eigenvalue problems for the nonsquare matrix pencils, proposed by Chu and Golub [SIAM J. Matrix Anal. Appl.<\/jats:italic>, 28(2006), pp. 770\u2010787], can be formulated as an optimization problem on a corresponding complex product Stiefel manifold. Some early proposed algorithms are based on the first\u2010order information of the objective function, and fast convergence could not be expected. In this article, we turn the generic Riemannian trust\u2010region method of Absil et al. into a practical algorithm for solving the underlying problem, which enjoys the global convergence and local superlinear convergence rate. Numerical experiments are provided to illustrate the efficiency of the proposed method. Detailed comparisons with some existing results (l<\/jats:italic>\u2009=\u20091 and l<\/jats:italic>\u2009=\u2009n<\/jats:italic>) are given first. For the case l<\/jats:italic>\u2009=\u2009n<\/jats:italic>, the algorithm can yield exactly the same optimal solution as Ito and Murota's algorithm, which is essentially a direct method to solve the problem. The algorithm runs faster than Boutry et al.'s algorithm for the case l<\/jats:italic>\u2009=\u20091. Further comparisons with some early proposed gradient\u2010based algorithms, and some latest infeasible methods for solving manifold optimization problems are also provided to show the merits of the proposed approach.<\/jats:p>","DOI":"10.1002\/nla.2363","type":"journal-article","created":{"date-parts":[[2021,2,17]],"date-time":"2021-02-17T18:07:35Z","timestamp":1613585255000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A trust\u2010region method for the parameterized generalized eigenvalue problem with nonsquare matrix pencils"],"prefix":"10.1002","volume":"28","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-7336-2980","authenticated-orcid":false,"given":"Jiao\u2010fen","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics and Computing Science, Center for Applied Mathematics of Guangxi (Guilin University of Electronic Technology), Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guangxi Key Laboratory of Automatic Detecting Technology and Instruments Guilin University of Electronic Technology Guilin China"}]},{"given":"Kai","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computing Science, Center for Applied Mathematics of Guangxi (Guilin University of Electronic Technology), Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guangxi Key Laboratory of Automatic Detecting Technology and Instruments Guilin University of Electronic Technology Guilin China"}]},{"given":"Yue\u2010yuan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computing Science, Center for Applied Mathematics of Guangxi (Guilin University of Electronic Technology), Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guangxi Key Laboratory of Automatic Detecting Technology and Instruments Guilin University of Electronic Technology Guilin China"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-3326-4585","authenticated-orcid":false,"given":"Xue\u2010feng","family":"Duan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computing Science, Center for Applied Mathematics of Guangxi (Guilin University of Electronic Technology), Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guangxi Key Laboratory of Automatic Detecting Technology and Instruments Guilin University of Electronic Technology Guilin China"}]},{"given":"Xue\u2010lin","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of International Exchange Guilin University of Electronic Technology Guilin China"}]}],"member":"311","published-online":{"date-parts":[[2021,2,14]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2005.10.006"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479803428795"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1137\/050628258"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drt021"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/060669267"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1137\/14099231X"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-018-1361-y"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2017.08.009"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1137\/0717073"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-019-01102-1"},{"key":"e_1_2_9_12_1","unstructured":"AbsilPA BakerCG GallivanKA. Trust\u2010region methods on Riemannian manifolds with applications in numerical linear algebra. Paper presented at: Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS2004). Leuven Belgium;2004. p. 5\u20139."},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-005-0179-9"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drn029"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1137\/090764827"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1080\/01630563.2011.618961"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.14495\/jsiaml.7.13"},{"key":"e_1_2_9_18_1","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2017.2723259"},{"key":"e_1_2_9_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2019.01.024"},{"key":"e_1_2_9_20_1","first-page":"406","volume-title":"Advances in neural information processing systems","author":"Boumal N","year":"2011"},{"key":"e_1_2_9_21_1","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2175"},{"key":"e_1_2_9_22_1","volume-title":"Matrix perturbation analysis","author":"Sun J","year":"2001"},{"key":"e_1_2_9_23_1","volume-title":"Optimization algorithms on matrix manifolds","author":"Absil PA","year":"2009"},{"key":"e_1_2_9_24_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479895290954"},{"key":"e_1_2_9_25_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-012-0584-1"},{"key":"e_1_2_9_26_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-016-9883-4"},{"key":"e_1_2_9_27_1","doi-asserted-by":"crossref","unstructured":"AbsilPA MahonyR TrumpfJ. An extrinsic look at the Riemannian Hessian. Proceedings of the International Conference on Geometric Science of Information. 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