When Lanczos Iterations Generate Symmetric Quadrature Nodes?
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917908985151488 |
|---|---|
| author | Li, Wenhao Han, Zongyuan Zhu, Shengxin |
| author_facet | Li, Wenhao Han, Zongyuan Zhu, Shengxin |
| contents | The Golub-Welsch algorithm [ Math. Comp., 23: 221-230 (1969)] has long been assumed symmetric for estimating quadratic forms. Recent research indicates that asymmetric quadrature nodes may be more often and the existence of a practical symmetric quadrature for estimating matrix quadratic form is even doubtful.This paper derives a sufficient condition for symmetric quadrature nodes for estimating quadratic forms involving the Jordan-Wielandt matrices which frequently arise from many applications. The condition is closely related to how to construct an initial vector for the underlying Lanczos process. Applications of such constructive results are demonstrated by estimating the Estrada index in complex network analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17757 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | When Lanczos Iterations Generate Symmetric Quadrature Nodes? Li, Wenhao Han, Zongyuan Zhu, Shengxin Numerical Analysis 65D32, 65F10, 65F15 The Golub-Welsch algorithm [ Math. Comp., 23: 221-230 (1969)] has long been assumed symmetric for estimating quadratic forms. Recent research indicates that asymmetric quadrature nodes may be more often and the existence of a practical symmetric quadrature for estimating matrix quadratic form is even doubtful.This paper derives a sufficient condition for symmetric quadrature nodes for estimating quadratic forms involving the Jordan-Wielandt matrices which frequently arise from many applications. The condition is closely related to how to construct an initial vector for the underlying Lanczos process. Applications of such constructive results are demonstrated by estimating the Estrada index in complex network analysis. |
| title | When Lanczos Iterations Generate Symmetric Quadrature Nodes? |
| topic | Numerical Analysis 65D32, 65F10, 65F15 |
| url | https://arxiv.org/abs/2401.17757 |