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Positive bidiagonal factorization of tetradiagonal Hessenberg matrices.
- Source :
-
Linear Algebra & its Applications . Nov2023, Vol. 677, p132-160. 29p. - Publication Year :
- 2023
-
Abstract
- Recently, a spectral Favard theorem was presented for bounded banded lower Hessenberg matrices that possess a positive bidiagonal factorization. The paper establishes conditions, expressed in terms of continued fractions, under which an oscillatory tetradiagonal Hessenberg matrix can have such a positive bidiagonal factorization. Oscillatory tetradiagonal Toeplitz matrices are examined as a case study of matrices that admit a positive bidiagonal factorization. Furthermore, the paper proves that oscillatory banded Hessenberg matrices are organized in rays, where the origin of the ray does not have a positive bidiagonal factorization, but all the interior points of the ray do have such a positive bidiagonal factorization. [ABSTRACT FROM AUTHOR]
- Subjects :
- *TOEPLITZ matrices
*NONNEGATIVE matrices
*CONTINUED fractions
*FACTORIZATION
Subjects
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 677
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 171901736
- Full Text :
- https://doi.org/10.1016/j.laa.2023.08.001