The parallel orbital-updating approach is an orbital/eigenfunction iteration based approach for solving eigenvalue problems when many eigenpairs are required. It has been proven to be efficient, for instance, in electronic structure calculations. In this paper, based on the investigation of a quasi-orthogonality, we present the numerical analysis of the parallel orbital-updating approach for linear eigenvalue problems, including convergence and error estimates of the numerical approximations.

Publication:

SIAM JOURNAL ON NUMERICAL ANALYSIS

http://dx.doi.org/10.1137/24M1690084

Author:

XIAOYING DAI

SKLMS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing,100190 China

School of Mathematical Sciences, University of Chinese Academy of Sciences,Beijing, 100049, China

daixy@lsec.cc.ac.cn

YAN LI

SKLMS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing,100190 China; and School of Mathematical Sciences, University of Chinese Academy of Sciences,Beijing, 100049, China

liyan2021@lsec.cc.ac.cn

BIN YANG

School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, 102206 China

binyang@lsec.cc.ac.cn

AIHUI ZHOU

SKLMS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing,100190 China; and School of Mathematical Sciences, University of Chinese Academy of Sciences,Beijing, 100049, China

azhou@lsec.cc.ac.cn