ON SMOOTH LU DECOMPOSITIONS WITH APPLICATIONS TO SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS  

作　　者：Hua Dai Zhong-Zhi Bai 

机构地区：[1]Department of Mathematics, Nanjing University of Aeronautics and Astronautics Nanjing 210016, China [2]LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences Beijing 100190, China

出　　处：《Journal of Computational Mathematics》2010年第6期745-766,共22页计算数学（英文）

基　　金：supported by the National Basic Research Program(No.2005CB321702);the China Outstanding Young Scientist F0undation(No.10525102);the National Natural Science Foundation (No.10471146),P.R.China

摘　　要：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.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.

关 键 词：Matrix-valued function Smooth LU decomposition PIVOTING Nonlinear eigenvalue problem Multiple eigenvalue Newton method. 

分 类 号：O177.2[理学—数学] O151.21[理学—基础数学]