Randomized quasi-Monte Carlo and Owen's boundary growth condition: A spectral analysis
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915290554564608 |
|---|---|
| author | Liu, Yang |
| author_facet | Liu, Yang |
| contents | In this work, we analyze the convergence rate of randomized quasi-Monte Carlo (RQMC) methods under Owen's boundary growth condition [Owen, 2006] via spectral analysis. Specifically, we examine the RQMC estimator variance for the two commonly studied sequences: the lattice rule and the Sobol' sequence, applying the Fourier transform and Walsh--Fourier transform, respectively, for this analysis. Assuming certain regularity conditions, our findings reveal that the asymptotic convergence rate of the RQMC estimator's variance closely aligns with the exponent specified in Owen's boundary growth condition for both sequence types. We also provide analysis for certain discontinuous integrands. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05181 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Randomized quasi-Monte Carlo and Owen's boundary growth condition: A spectral analysis Liu, Yang Numerical Analysis 65C05 In this work, we analyze the convergence rate of randomized quasi-Monte Carlo (RQMC) methods under Owen's boundary growth condition [Owen, 2006] via spectral analysis. Specifically, we examine the RQMC estimator variance for the two commonly studied sequences: the lattice rule and the Sobol' sequence, applying the Fourier transform and Walsh--Fourier transform, respectively, for this analysis. Assuming certain regularity conditions, our findings reveal that the asymptotic convergence rate of the RQMC estimator's variance closely aligns with the exponent specified in Owen's boundary growth condition for both sequence types. We also provide analysis for certain discontinuous integrands. |
| title | Randomized quasi-Monte Carlo and Owen's boundary growth condition: A spectral analysis |
| topic | Numerical Analysis 65C05 |
| url | https://arxiv.org/abs/2405.05181 |