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Name:  
Miloslav Znojil  
Reviewer number:  
9689  
Email:  
znojil@ujf.cas.cz  
Item's zblNumber:  
DE 0159 55102  
Author(s):  
Plestenjak, Bor:  
Shorttitle:  
A continuation method for a weakly elliptic twoparameter eigenvalue problem  
Source:  
IMA J. Numer. Anal. 21, No. 1, 199  216 (2001).  
Classification:  
 
Primary Classification:  
Secondary Classification:  
Keywords:  
eigenvalue problem; twoparametric matrix pencils; weakly elliptic; continuation method; homotopy bifurcation;  
Review:  
The method of solving eigenvalue problems for real nonsymmetric matrices as proposed by Li et al in 1992 is generalized to the twoparametric matrix pencils. The key idea remains the same (using an auxiliary parametric ``move" to a facilitated problem where all eigenvalues are algebraically simple) but the generalization is not easy (e.g., there exist no ``easy" curves of solutions anymore). A careful discussion is required and offered both on the theoretical level (paying attention to the cases where the matrices are large and/or where the algorithms have to be parallelized) and on the level of implementation (where, e.g., the numerical process can switch from one solution curve to another). In tests, a subtle balance is shown to exist between the number of recalculated continuation curves and the number of operations in the initial stage.  
Remarks to the editors:  