摘要
The locally optimal block preconditioned 4-d conjugate gradient method(LOBP4dC G) for the linear response eigenvalue problem was proposed by Bai and Li(2013) and later was extended to the generalized linear response eigenvalue problem by Bai and Li(2014). We put forward two improvements to the method: A shifting deflation technique and an idea of extending the search subspace. The deflation technique is able to deflate away converged eigenpairs from future computation, and the idea of extending the search subspace increases convergence rate per iterative step. The resulting algorithm is called the extended LOBP4 dC G(ELOBP4dC G).Numerical results of the ELOBP4 dC G strongly demonstrate the capability of deflation technique and effectiveness the search space extension for solving linear response eigenvalue problems arising from linear response analysis of two molecule systems.
The locally optimal block preconditioned 4-d conjugate gradient method （LOBP4dCG） for the linear response eigenvalue problem was proposed by Bai and Li （2013） and later was extended to the generalized linear response eigenvalue problem by Bai and Li （2014）. We put forward two improvements to the method： A shifting deflation technique and an idea of extending the search subspace. The deflation technique is able to deflate away converged eigenpairs from future computation, and the idea of extending the search subspace increases convergence rate per iterative step. The resulting algorithm is called the extended LOBP4dCG （ELOBP4dCG）. Numerical results of the ELOBP4dCG strongly demonstrate the capability of deflation technique and effec- tiveness the search space extension for solving linear response eigenvalue problems arising from linear response analysis of two molecule systems.
基金
supported by National Science Foundation of USA(Grant Nos.DMS1522697,CCF-1527091,DMS-1317330 and CCF-1527091)
National Natural Science Foundation of China(Grant No.11428104)
作者简介
Corresponding authorEmail： bai@cs, ucdavis, edu,rcli @uta. edu,wwlin@am. nctu. edu. tw
