Solving a Class of Nonlinear Eigenvalue Problems by Newton's Method
Lawrence Berkeley National Laboratory (Researcher), United States Department of Energy Office of Scientific and Technical Information (Distributor), Yang, Chao (Author), Meza, Juan C. (Author), Gao, Weiguo (Author), Computational Research Division (Sponsor)
We examine the possibility of using the standard Newton's method for solving a class of nonlinear eigenvalue problems arising from electronic structure calculation. We show that the Jacobian matrix associated with this nonlinear system has a special structure that can be exploited to reduce the computational complexity of the Newton's method. Preliminary numerical experiments indicate that the Newton's method can be more efficient for small problems in which a few smallest eigenpairs are needed
eBook, English, 2009
Lawrence Berkeley National Laboratory ; Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, Berkeley, Calif., Oak Ridge, Tenn., 2009