Spectral characterizations and integer powers of tridiagonal 2-Toeplitz matrices
In this note, we consider real nonsymmetric tridiagonal 2-Toeplitz matrices B n . First we give the asymptotic spectral and singular value distribution of the whole matrix-sequence { B n } n , which is described via two eigenvalue functions of a 2 × 2 matrix-valued symbol. In connection with the abo...
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| Vydáno v: | Numerical algorithms Ročník 100; číslo 2; s. 707 - 727 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.10.2025
Springer Nature B.V |
| Témata: | |
| ISSN: | 1017-1398, 1572-9265, 1572-9265 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | In this note, we consider real nonsymmetric tridiagonal 2-Toeplitz matrices
B
n
. First we give the asymptotic spectral and singular value distribution of the whole matrix-sequence
{
B
n
}
n
, which is described via two eigenvalue functions of a
2
×
2
matrix-valued symbol. In connection with the above findings, we provide a characterization of the eigenvalues and eigenvectors of real tridiagonal 2-Toeplitz matrices
B
n
of even order, that can be turned into a numerical effective scheme for the computation of all the entries of
B
n
l
,
n
even and
l
positive and small compared to
n
. We recall that a corresponding eigenvalue decomposition for odd order tridiagonal 2-Toeplitz matrices was found previously, while, for even orders, an implicit formula for all the eigenvalues is obtained. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1017-1398 1572-9265 1572-9265 |
| DOI: | 10.1007/s11075-024-01863-3 |