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基于区域排徐法和方格移动法的矩阵伪谱计算

周剑,蒋耀林   

  1. 西安交通大学理学院数学系;西安交通大学理学院数学系 西安710049;西安710049
  • 出版日期:2007-01-20 发布日期:2007-01-20

周剑,蒋耀林. 基于区域排徐法和方格移动法的矩阵伪谱计算[J]. 数值计算与计算机应用, 2007, 28(1): 71-80.

COMPUTATION OF MATRIX PSEUDOSPECTRA BY EXCLUSION REGIONS AND REMOTION PANE

  1. Zhou Jian Jiang Yaolin (Department of Mathematical Sciences,Xi'an Jiaotong University,Xi'an 710049,China)
  • Online:2007-01-20 Published:2007-01-20
常用的格子SVD法在精确计算矩阵A的ε-伪谱Λ_ε(A)时,需要将感兴趣的区域作细网格划分,在每一个网格点处计算σ_(min)(zI-A),并根据该值的大小判断该网格点是否位于Λ_ε(A)伪谱曲线上,其计算量往往很大.本文提出两种新的用于计算伪谱的方法:区域排除法和方格移动法.它们以不同方式,减小计算区域,大大提高了伪谱的计算速度.数值实验也充分说明算法的有效性.
The standard grid method(GRID),which is traditionally used to accurately compute theε-pseudospectrumΛ_ε(A)of a matrix A,is a process of highly de- manding computational task.At each point of domain of interest,the GRID computesσmin(zI-A)and uses that information in order to classify the point as belonging toΛ_ε(A)or not.It means that we shall pay much time for the computa- tion at those points out of the curve.In this paper,we provide two new methods to compute pseudospectra:exclusion regions and remotion pane.They could shrink the regions consumedly and accelerate the speed of computational process.Nu- merical experiments further show the effectiveness of the methods reported here.
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[1]L.N.Trefethen,Computation of pseudospectra,Acta Numerica,8(1999),247-295.
[2]J.K.Cullum and A.E.Ruehli,Pseudospectra analysis,nonlinear eigenvalue problems,and study- ing linear systems with delays,BIT,41:2(2001),265-281.
[3]Y.L.Jiang and O.Wing,A note on the spectra and pseudospectra of waveform relaxation operators for linear differential-algebraic equations,SIAM J.Numerical Analysis,38:1(2000), 186-201.
[4]T.Braconnier,R.A.McCoy,and V.Toumazou,Using the field of values for pseudospectra generation,Technical Report,TR/PA/97/28,CERFACS,Toulouse,1997.
[5]I.Koutis and E.Gallopoulos,Exclusion regions and fast estimation of pseudospectra,Technical Report,Department of Computer Engineering and Informatics,HP-CLAB,University of Patras, Greece,2000.
[6]C.Bekas and E.Gallopoulos,Parallel computation of pseudospectra by fast descent,Parallel Computing,28(2002),223-242.
[7]C.Bekas and E.Gallopoulos,Cobra:Parallel path following for computing the matrix pseu- dospectrum,Parallel Computing,27(2001),1879-1896.
[8]M.Br(?)hl,A curve tracing algorithm for computing the pseudospectrum,BIT,36:3(1996),441- 454.
[9]D.Mezher and B.Philippe,Parallel computation of pseudospectra of large sparse matrices,Par- allel Computing,28(2002),199-221.
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