Arnoldi versus nonsymmetric Lanczos algorithms for solving matrix eigenvalue problems

1996 ◽  
Vol 36 (3) ◽  
pp. 470-493 ◽  
Author(s):  
Jane Cullum
Keyword(s):  
Eigenvalue Problems ◽  
Matrix Eigenvalue ◽  
Matrix Eigenvalue Problems

Matrix Eigenvalue Problems

1965 ◽  
Vol 72 (sup2) ◽  
pp. 59-66
Author(s):  
Beresford Parlett
Keyword(s):  
Eigenvalue Problems ◽  
Matrix Eigenvalue ◽  
Matrix Eigenvalue Problems

scholarly journals Some Modified Matrix Eigenvalue Problems

SIAM Review ◽  
1973 ◽  
Vol 15 (2) ◽  
pp. 318-334 ◽  
Author(s):  
Gene H. Golub
Keyword(s):  
Eigenvalue Problems ◽  
Matrix Eigenvalue ◽  
Matrix Eigenvalue Problems

Real Asymmetric Matrix Eigenvalue Analysis for Dynamic Instability Problems

2000 ◽  
Author(s):  
Heewook Lee ◽  
Noboru Kikuchi
Keyword(s):  
Control Systems ◽  
Eigenvalue Problems ◽  
Dynamic Instability ◽  
Eigenvalue Analysis ◽  
Complex Eigenvalue ◽  
Friction Forces ◽  
Matrix Eigenvalue ◽  
Complex Eigenvalues ◽  
Complex Eigenvalue Analysis ◽  
Matrix Eigenvalue Problems

Abstract Complex eigenvalue analysis is widely used when the dynamic instability of the structure is in doubt due to friction forces, aerodynamic forces, control systems, or other effects. MSC/NASTRAN upper Hessenberg method and MATLAB eigenvalue solver produce fictitious nonzero real parts for real asymmetric matrix eigenvalue problems. For dynamic instability problems, since nonzero real parts of complex eigenvalues determine the unstable eigenvalues, the accuracy of real parts becomes crucial. The appropriate double shift QR or the QZ algorithms are applied to eliminate fictitious nonzero real parts and produce only authentic complex eigenvalues for real asymmetric matrix eigenvalue problems. Numerical examples are solved using the double shift QR and the QZ algorithms, and the results are compared with the results of MSC/NASTRAN upper Hessenberg method and MATLAB solvers.

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