A Lanczos Method for Large-Scale Extreme Lorentz Eigenvalue Problems
L.-H. Zhang, C. Shen, W.H. Yang and J. Júdice
Abstract
In
this paper, we are concerned with an efficient algorithm for solving
the Extreme Lorentz Eigenvalue problem (ELE). The Lorentz eigenvalue
problem is an eigenvalue complementary problem over the Lorentz cone,
and solving ELE is equivalent to testing the Lorentz-copositivity for a
given matrix. Treating ELE as a special eigenvalue problem, we propose
a Lanczos-type method which mimics the Rayleigh-Ritz procedure and is
suitable for large scale and sparse problems. The numerical behavior
and efficiency of the proposed method are supported by the theoretical
convergence results and some preliminary numerical experiments.