Name
Title | ||
|---|---|---|
On the condition numbers of a multiple eigenvalue of a generalized eigenvalue problem |
Abstract | ||
|---|---|---|
For standard eigenvalue problems, closed-form expressions for the condition numbers of a multiple eigenvalue are known. In particular, they are uniformly 1 in the Hermitian case and generally take different values in the non-Hermitian case. We consider the generalized eigenvalue problem and identify the condition numbers. Our main result is that a multiple eigenvalue generally has multiple condition numbers, even in the Hermitian definite case. The condition numbers are characterized in terms of the singular values of the outer product of the corresponding left and right eigenvectors. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1007/s00211-011-0440-x | Numerische Mathematik |
Keywords | Field | DocType |
multiple condition number,multiple eigenvalue,corresponding left,standard eigenvalue problem,generalized eigenvalue problem,hermitian case,closed-form expression,non-hermitian case,hermitian definite case,condition number,matrix theory | Singular value,Eigenvalue perturbation,Matrix (mathematics),Mathematical analysis,Eigendecomposition of a matrix,Divide-and-conquer eigenvalue algorithm,Hermitian matrix,Eigenvalues and eigenvectors,Mathematics,Inverse iteration | Journal |
Volume | Issue | ISSN |
121 | 3 | 0945-3245 |
Citations | PageRank | References |
0 | 0.34 | 3 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yuji Nakatsukasa | 1 | 97 | 17.74 |