Two-step Newton's method for deflation-one singular zeros of analytic systems
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914651774648320 |
|---|---|
| author | Lee, Kisun Li, Nan Zhi, Lihong |
| author_facet | Lee, Kisun Li, Nan Zhi, Lihong |
| contents | We propose a two-step Newton's method for refining an approximation of a singular zero whose deflation process terminates after one step, also known as a deflation-one singularity. Given an isolated singular zero of a square analytic system, our algorithm exploits an invertible linear operator obtained by combining the Jacobian and a projection of the Hessian in the direction of the kernel of the Jacobian. We prove the quadratic convergence of the two-step Newton method when it is applied to an approximation of a deflation-one singular zero. Also, the algorithm requires a smaller size of matrices than the existing methods, making it more efficient. We demonstrate examples and experiments to show the efficiency of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_10803 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Two-step Newton's method for deflation-one singular zeros of analytic systems Lee, Kisun Li, Nan Zhi, Lihong Numerical Analysis Symbolic Computation Algebraic Geometry 65D18, 14Q99 We propose a two-step Newton's method for refining an approximation of a singular zero whose deflation process terminates after one step, also known as a deflation-one singularity. Given an isolated singular zero of a square analytic system, our algorithm exploits an invertible linear operator obtained by combining the Jacobian and a projection of the Hessian in the direction of the kernel of the Jacobian. We prove the quadratic convergence of the two-step Newton method when it is applied to an approximation of a deflation-one singular zero. Also, the algorithm requires a smaller size of matrices than the existing methods, making it more efficient. We demonstrate examples and experiments to show the efficiency of the method. |
| title | Two-step Newton's method for deflation-one singular zeros of analytic systems |
| topic | Numerical Analysis Symbolic Computation Algebraic Geometry 65D18, 14Q99 |
| url | https://arxiv.org/abs/2305.10803 |