Inexact Newton preconditioning techniques for large symmetric eigenvalue problems.

Wu, Kesheng; Saad, Yousef; Stathopoulos, Andreas

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Quasi-Newton preconditioners for the inexact Newton method.

Bergamaschi, L., Bru, R., Martínez, A., Putti, M. (2006)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

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A full-Newton approach to separable nonlinear least squares problems and its application to discrete least squares rational approximation.

Borges, Carlos F. (2009)

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A multilevel Newton's method for eigenvalue problems

Yunhui He, Yu Li, Hehu Xie, Chun&#039;guang You, Ning Zhang (2018)

Applications of Mathematics

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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...

Two-level nonlinear elimination based preconditioners for inexact Newton methods with application in shocked duct flow calculation.

Hwang, Feng-Nan, Lin, Hsin-Lun, Cai, Xiao-Chuan (2010)

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Robust preconditioners for the matrix free truncated Newton method

Lukšan, Ladislav, Matonoha, Ctirad, Vlček, Jan

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New positive definite preconditioners for the matrix free truncated Newton method are given. Corresponding algorithms are described in detail. Results of numerical experiments that confirm the efficiency and robustness of the preconditioned truncated Newton method are reported.