A method for computing all values λ such thatA+λBhas a multiple eigenvalue
| Autor: | Bor Plestenjak, Andrej Muhič |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Numerical Analysis
Numerical linear algebra Algebra and Number Theory Kronecker canonical form Mathematical analysis computer.software_genre Combinatorics Matrix (mathematics) Discrete Mathematics and Combinatorics Geometry and Topology Divide-and-conquer eigenvalue algorithm computer Pencil (mathematics) Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Linear Algebra and its Applications. 440:345-359 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2013.10.015 |
| Popis: | Given a pair of n × n matrices A and B, we consider the problem of finding values λ such that the matrix A + λ B has a multiple eigenvalue. Our approach solves the problem using only the standard matrix computation tools. By formulating the problem as a singular two-parameter eigenvalue problem, we construct matrices Δ 1 and Δ 0 of size 3 n 2 × 3 n 2 with the property that the finite regular eigenvalues of the singular pencil Δ 1 − λ Δ 0 are the values λ such that A + λ B has a multiple eigenvalue. We show that these values can be computed numerically from Δ 1 and Δ 0 by the staircase algorithm. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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