標題: DOUBLING ALGORITHM FOR THE DISCRETIZED BETHE-SALPETER EIGENVALUE PROBLEM
作者: Guo, Zhen-Chen
Chu, Eric King-Wah
Lin, Wen-Wei
應用數學系
Department of Applied Mathematics
關鍵字: Bethe-Salpeter eigenvalue problem;Cayley transform;doubling algorithm
公開日期: 1-Sep-2019
摘要: The discretized Bethe-Salpeter eigenvalue problem arises in the Green's function evaluation in many body physics and quantum chemistry. Discretization leads to a matrix eigenvalue problem for H is an element of C-2n(x2n) with a Hamiltonian-like structure. After an appropriate transformation of H to a standard symplectic form, the structure-preserving doubling algorithm, originally for algebraic Riccati equations, is extended for the discretized Bethe-Salpeter eigenvalue problem. Potential breakdowns of the algorithm, due to the ill condition or singularity of certain matrices, can be avoided with a double-Cayley transform or a three-recursion remedy. A detailed convergence analysis is conducted for the proposed algorithm, especially on the benign effects of the double-Cayley transform. Numerical results are presented to demonstrate the efficiency and the structure-preserving nature of the algorithm.
URI: http://dx.doi.org/10.1090/mcom/3398
http://hdl.handle.net/11536/152424
ISSN: 0025-5718
DOI: 10.1090/mcom/3398
期刊: MATHEMATICS OF COMPUTATION
Volume: 88
Issue: 319
起始頁: 2325
結束頁: 2350
Appears in Collections:Articles