A multilevel Newton's method for eigenvalue problems
Applications of Mathematics, Tome 63 (2018) no. 3, pp. 281-303.

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We propose a new type of multilevel method for solving eigenvalue problems based on Newton's method. With the proposed iteration method, solving an eigenvalue problem on the finest finite element space is replaced by solving a small scale eigenvalue problem in a coarse space and a sequence of augmented linear problems, derived by Newton step in the corresponding sequence of finite element spaces. This iteration scheme improves overall efficiency of the finite element method for solving eigenvalue problems. Finally, some numerical examples are provided to validate the efficiency of the proposed numerical scheme.
DOI : 10.21136/AM.2018.0086-18
Classification : 65B99, 65L15, 65N25, 65N30
Keywords: eigenvalue problem; finite element method; Newton's method; multilevel iteration
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     title = {A multilevel {Newton's} method for eigenvalue problems},
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He, Yunhui; Li, Yu; Xie, Hehu; You, Chun'guang; Zhang, Ning. A multilevel Newton's method for eigenvalue problems. Applications of Mathematics, Tome 63 (2018) no. 3, pp. 281-303. doi : 10.21136/AM.2018.0086-18. http://geodesic.mathdoc.fr/articles/10.21136/AM.2018.0086-18/

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