伪谱计算的降维迭代算法（英文）  

COMPUTING PSEUDOSPECTRA USING INDUCED DIMENSION REDUCTION ITERATION

作　　者：左钱 王正盛[1] 何颖 Zuo Qian;Wang Zhengsheng;He Ying(College of Science, Nanjing University of Aeronautics and Astronautics,Nanjing 210016)

机构地区：[1]南京航空航天大学理学院,南京210016

出　　处：《高等学校计算数学学报》2019年第1期1-14,共14页Numerical Mathematics A Journal of Chinese Universities

基　　金：supported by the National Natural Science Foundation of China under grant No.11571171 and No.61473148~~

摘　　要：The pseudospectra is a helpful tool to analyze the behavior of systems involved with non-normal matrices or linear operators. In this paper, we present a new method to approximate the pseudospetra of large scale matrices. Using the Induced Dimension Reduction iteration(IDR), which was originally proposed for solving systems of linear equations, then we obtain a Hessenberg decomposition,from which we approximate the pseudospectra of a matrix since the IDR iteration is a short-recurrence method which is attractive for large scale computations. Additionally, the IDR polynomial create this Hessenberg decomposition is also used as a filter to discard the unwanted eigenvalues, which is specially constructive and meaningful for computing pseudospectra of large matrices. Numerical experiments and comparisons on the test matrices from the literature show that the proposed method is much more efficient than the Grid-SVD method, inverse Lanczos method,and the implicitly restarted Arnoldi method(IRAM).The pseudospectra is a helpful tool to analyze the behavior of systems involved with non-normal matrices or linear operators. In this paper, we present a new method to approximate the pseudospetra of large scale matrices. Using the Induced Dimension Reduction iteration(IDR), which was originally proposed for solving systems of linear equations, then we obtain a Hessenberg decomposition,from which we approximate the pseudospectra of a matrix since the IDR iteration is a short-recurrence method which is attractive for large scale computations. Additionally, the IDR polynomial create this Hessenberg decomposition is also used as a filter to discard the unwanted eigenvalues, which is specially constructive and meaningful for computing pseudospectra of large matrices. Numerical experiments and comparisons on the test matrices from the literature show that the proposed method is much more efficient than the Grid-SVD method, inverse Lanczos method,and the implicitly restarted Arnoldi method(IRAM).

关 键 词：PSEUDOSPECTRA Induced DIMENSION Reduction SVD. 

分 类 号：O241.6[理学—计算数学]