Stochastic Diagonal Estimation Based on Matrix Quadratic Form Oracles
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918062852145152 |
|---|---|
| author | Ye, Haishan Chang, Xiangyu |
| author_facet | Ye, Haishan Chang, Xiangyu |
| contents | We study the problem of estimating the diagonal of an implicitly given matrix $\Ab$. For such a matrix we have access to an oracle that allows us to evaluate the matrix quadratic form $ \ub^\top \Ab \ub$. Based on this query oracle, we propose a stochastic diagonal estimation method with random variable $\ub$ drawn from the standard Gaussian distribution. We provide the element-wise and norm-wise sample complexities of the proposed method. Our numerical experiments on different types and dimensions matrices demonstrate the effectiveness of our method and validate the tightness of theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15360 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic Diagonal Estimation Based on Matrix Quadratic Form Oracles Ye, Haishan Chang, Xiangyu Numerical Analysis We study the problem of estimating the diagonal of an implicitly given matrix $\Ab$. For such a matrix we have access to an oracle that allows us to evaluate the matrix quadratic form $ \ub^\top \Ab \ub$. Based on this query oracle, we propose a stochastic diagonal estimation method with random variable $\ub$ drawn from the standard Gaussian distribution. We provide the element-wise and norm-wise sample complexities of the proposed method. Our numerical experiments on different types and dimensions matrices demonstrate the effectiveness of our method and validate the tightness of theoretical results. |
| title | Stochastic Diagonal Estimation Based on Matrix Quadratic Form Oracles |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2506.15360 |