The geometry of matrix eigenvalue methods. (English) Zbl 0639.34046
The authors introduce what they claim to be a natural geometric setting for studying the numerical matrix eigenvalue methods. The mathematical tools used in establishing this setting come from the theory of Lie transformation groups and the analysis of the relations between the matrix Riccati equation and the standard matrix eigenvalue methods. The paper opens up an interesting research line in the use of differential geometry in the study of matrix eigenvalue methods.
Reviewer: U.D’Ambrosio
MSC:
| 53C30 | Differential geometry of homogeneous manifolds |
| 37N99 | Applications of dynamical systems |
| 57S25 | Groups acting on specific manifolds |
Keywords:
flag manifold; algorithm; numerical matrix eigenvalue methods; Lie transformation groups; matrix Riccati equationReferences:
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