Zentralblatt MATH - REVIEW SUBMISSION FORM
Zentralblatt MATH HOME

Your review has been received.

Thank you very much.

(You may want so save a copy of this page for your files.)

Name:
Miloslav Znojil
Reviewer number:
9689
Email:
znojil@ujf.cas.cz
Item's zbl-Number:
DE 0159 55102
Author(s):
Plestenjak, Bor:
Shorttitle:
A continuation method for a weakly elliptic two-parameter eigenvalue problem
Source:
IMA J. Numer. Anal. 21, No. 1, 199 - 216 (2001).
Classification:
65F15Eigenvalues, eigenvectors
Primary Classification:
Secondary Classification:
Keywords:
eigenvalue problem; two-parametric matrix pencils; weakly elliptic; continuation method; homotopy bifurcation;
Review:

The method of solving eigenvalue problems for real non-symmetric
matrices as proposed by Li et al in 1992 is generalized to the
two-parametric 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
re-calculated continuation curves and the number of operations in
the initial stage.
Remarks to the editors:

(New formular )