二次特征值问题中等导特征对的灵敏度分析  

Sensitivity analysis of repeated eigenpairs with equal derivatives of quadratic eigenvalue problems

作　　者：王平心 吴颉尔 杨习贝[3] WANG Pingxin;WU Jieer;YANG Xibei(School of Science,Jiangsu University of Science and Technology,Zhenjiang 212003,China;School of Computer Science,Jiangsu University of Science and Technology,Zhenjiang 212003,China;College of Mathematics and Information Science,Hebei Normal University,Shijiazhuang 050024,China)

机构地区：[1]江苏科技大学理学院,镇江212003 [2]河北师范大学数学与信息科学理学院,石家庄050024 [3]江苏科技大学计算机学院,镇江212003

出　　处：《江苏科技大学学报（自然科学版）》2018年第5期753-758,共6页Journal of Jiangsu University of Science and Technology:Natural Science Edition

基　　金：国家自然科学基金资助项目(61503160;61572242);江苏省高校自然科学基金资助项目(15KJB110004)

摘　　要：特征对导数的计算是特征灵敏度分析的主要研究内容之一.文中利用矩阵广义逆理论导出了一种计算对称二次特征问题重特征值在等导情况下特征对导数的新算法.该算法将特征向量导数表示为支配方程的特解和对应齐次方程的通解之和,然后利用矩阵广义逆分别计算支配方程的特解和相应齐次方程的解.数值例子结果表明算法在计算等导特征对导数的问题上是有效的.The computation of derivatives of eigenvalues and corresponding eigenvectors is one of the main objects for sensitivity analysis of eigenvalue problems.By using generalized inverse of matrix,this paper presents a new algorithm for computing the derivatives of the semisimple eigenvalues with equal derivatives and corresponding eigenvectors of quadratic eigenvalue problems.In the proposed method,the derivatives of eigenvectors are divided into a particular solution of the governed equations and a general solution of the corresponding homogeneous equations,where the particular solution is constructed by using generalized inverse.The effectiveness of the proposed algorithm is illustrated by one numerical example.

关 键 词：二次特征值问题 等导 特征值导数 特征向量导数 

分 类 号：O241.6[理学—计算数学]