Browsing by Author "Guo, Zhen-Chen"

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DOUBLING ALGORITHM FOR THE DISCRETIZED BETHE-SALPETER EIGENVALUE PROBLEM
(2019-09-01)
Guo, Zhen-Chen
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Chu, Eric King-Wah
;
Lin, Wen-Wei
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應用數學系
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Department of Applied Mathematics
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.
Schur method for robust pole assignment of descriptor systems via proportional plus derivative state feedback
(2019-10-03)
Guo, Zhen-Chen
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丘成桐中心
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Shing-Tung Yau Center
The pole assignment problem for descriptor systems is a classical inverse algebraic eigenvalue problem, which has attracted attention for decades. In this paper, we propose a direct method to solve the problem with the application of the proportional plus derivative state feedback, intending to obtain a robust closed-loop system. Theorems on the feasibility of our method will be presented. Numerical examples show that our method yields poles of high relative accuracy.
Structure-preserving Gamma QR and Gamma-Lanczos algorithms for Bethe-Salpeter eigenvalue problems
(2018-10-15)
Guo, Zhen-Chen
;
Li, Tiexiang
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Zhou, Ying-Ying
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應用數學系
;
Department of Applied Mathematics
To solve the Bethe-Salpeter eigenvalue problem with distinct sizes, two efficient methods, called Gamma QR algorithm and Gamma-Lanczos algorithm, are proposed in this paper. Both algorithms preserve the special structure of the initial matrix. H = [(-(B) over bar) (A) (-(A) over bar) (B)], resulting the computed eigenvalues and the associated eigenvectors still hold the properties similar to those of dr. Theorems are given to demonstrate the validity of the proposed two algorithms in theory. Numerical results are presented to illustrate the superiorities of our methods. (C) 2018 Elsevier B.V. All rights reserved.