Random Walks, Faber Polynomials and Accelerated Power Methods
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914544265199616 |
|---|---|
| author | Cowal, Peter Marshall, Nicholas F. Pollock, Sara |
| author_facet | Cowal, Peter Marshall, Nicholas F. Pollock, Sara |
| contents | In this paper, we construct families of polynomials defined by recurrence relations related to mean-zero random walks. We show these families of polynomials can be used to approximate $z^n$ by a polynomial of degree $\sim \sqrt{n}$ in associated radially convex domains in the complex plane. Moreover, we show that the constructed families of polynomials have a useful rapid growth property and a connection to Faber polynomials. Applications to iterative linear algebra are presented, including the development of arbitrary-order dynamic momentum power iteration methods suitable for classes of non-symmetric matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24608 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Random Walks, Faber Polynomials and Accelerated Power Methods Cowal, Peter Marshall, Nicholas F. Pollock, Sara Numerical Analysis 30E10, 65F15, 68Q87 In this paper, we construct families of polynomials defined by recurrence relations related to mean-zero random walks. We show these families of polynomials can be used to approximate $z^n$ by a polynomial of degree $\sim \sqrt{n}$ in associated radially convex domains in the complex plane. Moreover, we show that the constructed families of polynomials have a useful rapid growth property and a connection to Faber polynomials. Applications to iterative linear algebra are presented, including the development of arbitrary-order dynamic momentum power iteration methods suitable for classes of non-symmetric matrices. |
| title | Random Walks, Faber Polynomials and Accelerated Power Methods |
| topic | Numerical Analysis 30E10, 65F15, 68Q87 |
| url | https://arxiv.org/abs/2510.24608 |