Abstract
In this paper, by the use of the residual vector and an approximation to the steepest descent direction of the norm function, we develop a norm descent spectral method for solving symmetric nonlinear equations. The method based on the nomonotone line search techniques is showed to be globally convergent. A specific implementation of the method is given which exploits the recently developed cyclic Barzilai–Borwein (CBB) for unconstrained optimization. Preliminary numerical results indicate that the method is promising.
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Supported by the NSF of China via grant 11071087, 11101081 and by Foundation for Distinguished Young Talents in Higher Education of Guangdong, China LYM10127 and the NSF of Dongguan University of Technology via grant ZN100024.
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Cheng, W., Chen, Z. Nonmonotone spectral method for large-scale symmetric nonlinear equations. Numer Algor 62, 149–162 (2013). https://doi.org/10.1007/s11075-012-9572-z
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DOI: https://doi.org/10.1007/s11075-012-9572-z