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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.00016 |
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| _version_ | 1866910313478094848 |
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| author | Lashomb, Paul Morgan, Ronald B. Whyte, Travis Wilcox, Walter |
| author_facet | Lashomb, Paul Morgan, Ronald B. Whyte, Travis Wilcox, Walter |
| contents | In lattice QCD the calculation of disconnected quark loops from the trace of the inverse quark matrix has large noise variance. A multilevel Monte Carlo method is proposed for this problem that uses different degree polynomials on a multilevel system. The polynomials are developed from the GMRES algorithm for solving linear equations. To reduce orthogonalization expense, the highest degree polynomial is a composite or double polynomial found with a polynomial preconditioned GMRES iteration. Matrix deflation is used in three different ways: in the Monte Carlo levels, in the main solves, and in the deflation of the highest level double polynomial. A numerical comparison with optimized Hutchinson is performed on a quenched \(24^4\) lattice. The results demonstrate that the new Multipolynomial Monte Carlo method can significantly improve the trace computation for matrices that have a difficult spectrum due to small eigenvalues.} |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00016 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multipolynomial Monte Carlo Trace Estimation Lashomb, Paul Morgan, Ronald B. Whyte, Travis Wilcox, Walter High Energy Physics - Lattice Mathematical Physics In lattice QCD the calculation of disconnected quark loops from the trace of the inverse quark matrix has large noise variance. A multilevel Monte Carlo method is proposed for this problem that uses different degree polynomials on a multilevel system. The polynomials are developed from the GMRES algorithm for solving linear equations. To reduce orthogonalization expense, the highest degree polynomial is a composite or double polynomial found with a polynomial preconditioned GMRES iteration. Matrix deflation is used in three different ways: in the Monte Carlo levels, in the main solves, and in the deflation of the highest level double polynomial. A numerical comparison with optimized Hutchinson is performed on a quenched \(24^4\) lattice. The results demonstrate that the new Multipolynomial Monte Carlo method can significantly improve the trace computation for matrices that have a difficult spectrum due to small eigenvalues.} |
| title | Multipolynomial Monte Carlo Trace Estimation |
| topic | High Energy Physics - Lattice Mathematical Physics |
| url | https://arxiv.org/abs/2402.00016 |