Duminil, Sébastien; Sadok, Hassane Reduced rank extrapolation applied to electronic structure computations. (English) Zbl 1287.65040 ETNA, Electron. Trans. Numer. Anal. 38, 347-362 (2011). Summary: This paper presents a new approach for accelerating the convergence of a method for solving a nonlinear eigenvalue problem that arises in electronic structure computations. Specifically, we seek to solve the Schrödinger equation using the Kohn-Sham formulation. This requires the solution of a nonlinear eigenvalue problem. The currently prevailing method for determining an approximate solution is the self-consistent field method accelerated by Anderson’s iterative procedure or a Broyden-type method. We propose to formulate the nonlinear eigenvalue problem as a nonlinear fixed point problem and to accelerate the convergence of fixed-point iteration by vector extrapolation. We revisit the reduced rank extrapolation method, a polynomial-type vector extrapolation method, and apply it in the real-space density functional theory software. Cited in 5 Documents MSC: 65H17 Numerical solution of nonlinear eigenvalue and eigenvector problems 35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs 35Q55 NLS equations (nonlinear Schrödinger equations) Keywords:nonlinear eigenvalue problem; vector extrapolation; Kohn-Sham equation; reduced rank extrapolation; convergence acceleration; electronic structure computation; Schrödinger equation; self-consistent field method; Anderson’s iterative procedure; Broyden-type method; real-space density functional theory software Software:KSSOLV PDFBibTeX XMLCite \textit{S. Duminil} and \textit{H. Sadok}, ETNA, Electron. Trans. Numer. Anal. 38, 347--362 (2011; Zbl 1287.65040) Full Text: EMIS