THE MATRIX EQUATION X + ATX-1 A = Q AND ITS APPLICATION IN NANO RESEARCH

被引：27

作者：

Guo, Chun-Hua ^{[1
]}

Lin, Wen-Wei ^{[2
]}

机构：

[1] Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2, Canada

[2] Natl Chiao Tung Univ, Dept Appl Math, Hsinchu 300, Taiwan

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2010年 / 32卷 / 05期

基金：

加拿大自然科学与工程研究理事会;

关键词：

nonlinear matrix equation; complex symmetric solution; stable solution; fixed-point iteration; doubling algorithm; Newton's method; Green's function; CONVERGENCE ANALYSIS; EIGENVALUE PROBLEMS;

D O I：

10.1137/090758209

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The matrix equation X + A(T)X(-1) A = Q has been studied extensively when A and Q are real square matrices and Q is symmetric positive definite. The equation has positive definite solutions under suitable conditions, and in that case the solution of interest is the maximal positive definite solution. The same matrix equation plays an important role in Green's function calculations in nano research, but the matrix Q there is usually indefinite (so the matrix equation has no positive definite solutions), and one is interested in the case where the matrix equation has no positive definite solutions even when Q is positive definite. The solution of interest in this nano application is a special weakly stabilizing complex symmetric solution. In this paper we show how a doubling algorithm can be used to find good approximations to the desired solution efficiently and reliably.

引用

页码：3020 / 3038

页数：19

共 50 条

[21] The iterative methods for solving nonlinear matrix equation X plus A☆X-1A plus B☆X-1B = Q
Vaezzadeh, Sarah
Vaezpour, Seyyed Mansour
Saadati, Reza
Park, Choonkil
ADVANCES IN DIFFERENCE EQUATIONS, 2013,
[22] On the Sensitivity Estimation of the Matrix Equation X-s +/- A* X-t A = Q
Popchev, Ivan
Angelova, Vera
CYBERNETICS AND INFORMATION TECHNOLOGIES, 2010, 10 (02) : 14 - 30
[23] On positive definite solutions of the matrix equation X - Σi =1m Ai* X-piAi = Q
Li, Changzhou
Yuan, Chao
Chen, Shiliang
AIMS MATHEMATICS, 2024, 9 (09): : 25532 - 25544
[24] On solutions for the matrix equation Xs+A*X-t A=Q
Yang, Yueting
Duan, Fujian
Zhao, Xue
ADVANCES IN MATRIX THEORY AND APPLICATIONS, 2006, : 20 - 23
[25] Positive definite solution of the matrix equation X = Q + AH (I ⊗ X - C)δ A
Yao, Guozhu
Liao, Anping
Duan, Xuefeng
NUMERICAL ALGORITHMS, 2011, 56 (03) : 349 - 361
[26] POSITIVE DEFINITE SOLUTION OF THE MATRIX EQUATION X = Q + AH(I ⊗ X - C)-δ A
Yao, Guozhu
Liao, Anping
Duan, Xuefeng
ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2010, 21 : 76 - 84
[27] On the Sensitivity of the Matrix Equations X +/- A* X-1 A = Q
Popchev, Ivan
Angelova, Vera
CYBERNETICS AND INFORMATION TECHNOLOGIES, 2010, 10 (04) : 36 - 61
[28] On Hermitian positive definite solution of the matrix equation X - Σi=1mAi*XrAi = Q
Duan, Xuefeng
Liao, Anping
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 229 (01) : 27 - 36
[29] On the Nonlinear Matrix Equation X+A;f;（X）A+B;f;（X）B=Q
Sang Hai-feng
Liu Pan-pan
Zhang Shu-gong
Li Qing-chun
Ma Fu-ming
Communications in Mathematical Research, 2013, 29 (03) : 280 - 288
[30] On the Theory of Nonlinear Matrix Equation Xs = Q + AH(I ⊗ X - C)-δ A
Liu, Wei
Sang, Haifeng
Li, Qingchun
Zhai, Chunwei
BIO-INSPIRED COMPUTING - THEORIES AND APPLICATIONS, BIC-TA 2014, 2014, 472 : 281 - 288

← 1 2 3 4 5 →