ON SMOOTH LU DECOMPOSITIONS WITH APPLICATIONS TO SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS
查看参考文献43篇
|
文摘
|
We study the smooth LU decomposition of a given analytic functional A-matrix A(A) and its block-analogue. Sufficient conditions for the existence of such matrix decompositions are given, some differentiability about certain elements arising from them are proved, and several explicit expressions for derivatives of the specified elements are provided. By using these smooth LU decompositions, we propose two numerical methods for computing multiple nonlinear eigenvalues of A(A), and establish their locally quadratic convergence properties. Several numerical examples are provided to show the feasibility and effectiveness of these new methods. Mathematics subject classification: 15A18, 15A23, 65F15 |
|
来源
|
Journal of Computational Mathematics
,2010,28(6):745-766 【核心库】
|
|
DOI
|
10.4208/jcm.1004-m0009
|
|
关键词
|
Matrix-valued function
;
Smooth LU decomposition
;
Pivoting
;
Nonlinear eigenvalue problem
;
Multiple eigenvalue
;
Newton method
|
|
地址
|
1.
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016
2.
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190
|
|
语种
|
英文 |
|
文献类型
|
研究性论文 |
|
ISSN
|
0254-9409 |
|
学科
|
数学 |
|
基金
|
国家973计划
;
国家自然科学基金国家杰出青年科学基金
;
国家自然科学基金
|
|
文献收藏号
|
CSCD:4044167
|
参考文献 共
43
共3页
|
|
1.
Andrew A.L. On the numerical solution of nonlinear eigenvalue problems.
Computing,1995,55:91-111
|
CSCD被引
3
次
|
|
|
|
|
2.
Anselone P.M. The solution of characteristic value-vector problems by Newton's method.
Numerische Mathematik,1968,11:38-45
|
CSCD被引
1
次
|
|
|
|
|
3.
Barrlund A. Perturbation bounds for the LDLH and LU decompositions.
BIT Numer. Math,1991,31:358-363
|
CSCD被引
2
次
|
|
|
|
|
4.
Bendtsen C. Solving large nonlinear generalized eigenvalue problems from density functional theory calculations in parallel.
Appl. Numer. Math,2001,37:189-199
|
CSCD被引
3
次
|
|
|
|
|
5.
Betcke T. A Jacobi-Davidson-type projection method for nonlinear eigenvalue problems.
Future Gener. Comput. Sys,2004,20:363-372
|
CSCD被引
6
次
|
|
|
|
|
6.
Bunse-Gerstner A. Numerical computation of an analytic singular value decomposition of a matrix valued function.
Numerische Mathematik,1991,60:1-39
|
CSCD被引
1
次
|
|
|
|
|
7.
Chan T.F. On the existence and computation of LU-factorizations with small pivots.
Math. Comput,1984,42:535-547
|
CSCD被引
1
次
|
|
|
|
|
8.
Dai H. Numerical methods for finding multiple eigenvalues of matrices depending on parameters.
Numerische Mathematik,1997,76:189-208
|
CSCD被引
1
次
|
|
|
|
|
9.
Daya E.M. A numerical method for nonlinear eigenvalue problems application to vibrations of viscoelastic structures.
Comput. Struct,2001,79:533-541
|
CSCD被引
5
次
|
|
|
|
|
10.
Dieci L. On smooth decompositions of matrices.
SIAM J. Matrix Anal. Appl,1999,20:800-819
|
CSCD被引
1
次
|
|
|
|
|
11.
N A Dumont. On the solution of generalized non-linear complex-symmetric eigenvalue problems.
Int. J. Numer. Meth. Engrg,2007,71:1534-1568
|
CSCD被引
2
次
|
|
|
|
|
12.
Fletcher R.
Practical Methods of Optimization, Vol. 1: Unconstrained Optimization,1980
|
CSCD被引
1
次
|
|
|
|
|
13.
Gingold H. Globally analytic triangularization of a matrix function.
Linear Algebra Appl,1992,169:75-101
|
CSCD被引
1
次
|
|
|
|
|
14.
Golub G.H.
Matrix Computations, 3rd ed,1996
|
CSCD被引
17
次
|
|
|
|
|
15.
Guo J.-S. Nonequivalence deflation for the solution of matrix latent value problems.
Linear Algebra Appl,1995,231:15-45
|
CSCD被引
3
次
|
|
|
|
|
16.
Horn R A.
Matrix Analysis,1985
|
CSCD被引
391
次
|
|
|
|
|
17.
Hwang T-M. Rank revealing LU factorizations.
Linear Algebra Appl,1992,175:115-141
|
CSCD被引
1
次
|
|
|
|
|
18.
Hwang T-M. Improved bound for rank revealing LU factorizations.
Linear Algebra Appl,1997,261:173-186
|
CSCD被引
1
次
|
|
|
|
|
19.
Hwang T-M. Jacobi-Davidson methods for cubic eigenvalue problems.
Numer. Linear Algebra Appl,2005,12:605-624
|
CSCD被引
1
次
|
|
|
|
|
20.
N K Jain. On Kublanovskaya's approach to the solution of the generalized latent value problem for functional A-matrices.
SIAM J. Numer. Anal,1983,20:1062-1070
|
CSCD被引
3
次
|
|
|
|
|
了解气象卫星更多信息，请访问