Generation of non-uniform low-discrepancy sequences in the multidimensional case
In this paper we extend the results we obtained in an earlier paper, from the one-dimensional case to the \(s\)-dimensional case. We propose two inversion type methods for generating \(G\)-distributed low-discrepancy sequences in \([0,1]^{s}\), where \(G\) is an arbitrary distribution function. Our...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2006-08-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
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| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/847 |
| _version_ | 1818529307989901312 |
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| author | Natalia Roşca |
| author_facet | Natalia Roşca |
| author_sort | Natalia Roşca |
| collection | DOAJ |
| description | In this paper we extend the results we obtained in an earlier paper, from the one-dimensional case to the \(s\)-dimensional case. We propose two inversion type methods for generating \(G\)-distributed low-discrepancy sequences in \([0,1]^{s}\), where \(G\) is an arbitrary distribution function. Our methods are based on the approximation of the inverses of the marginal distribution functions using linear Lagrange interpolation or cubic Hermite interpolation. We also determine upper bounds for the \(G\)-discrepancy of the sequences we generate using the proposed methods. |
| first_indexed | 2024-12-11T17:05:13Z |
| format | Article |
| id | doaj.art-bb15f9488a314e9b834e0fc0cab3a779 |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-12-11T17:05:13Z |
| publishDate | 2006-08-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-bb15f9488a314e9b834e0fc0cab3a7792022-12-22T00:57:43ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2006-08-01352Generation of non-uniform low-discrepancy sequences in the multidimensional caseNatalia Roşca0“Babes-Bolyai” University, RomaniaIn this paper we extend the results we obtained in an earlier paper, from the one-dimensional case to the \(s\)-dimensional case. We propose two inversion type methods for generating \(G\)-distributed low-discrepancy sequences in \([0,1]^{s}\), where \(G\) is an arbitrary distribution function. Our methods are based on the approximation of the inverses of the marginal distribution functions using linear Lagrange interpolation or cubic Hermite interpolation. We also determine upper bounds for the \(G\)-discrepancy of the sequences we generate using the proposed methods.https://ictp.acad.ro/jnaat/journal/article/view/847discrepancyuniformly distributed sequences\(G\)-discrepancy\(G\)-distributed sequenceslow-discrepancy sequencesquasi-Monte Carlo integration |
| spellingShingle | Natalia Roşca Generation of non-uniform low-discrepancy sequences in the multidimensional case Journal of Numerical Analysis and Approximation Theory discrepancy uniformly distributed sequences \(G\)-discrepancy \(G\)-distributed sequences low-discrepancy sequences quasi-Monte Carlo integration |
| title | Generation of non-uniform low-discrepancy sequences in the multidimensional case |
| title_full | Generation of non-uniform low-discrepancy sequences in the multidimensional case |
| title_fullStr | Generation of non-uniform low-discrepancy sequences in the multidimensional case |
| title_full_unstemmed | Generation of non-uniform low-discrepancy sequences in the multidimensional case |
| title_short | Generation of non-uniform low-discrepancy sequences in the multidimensional case |
| title_sort | generation of non uniform low discrepancy sequences in the multidimensional case |
| topic | discrepancy uniformly distributed sequences \(G\)-discrepancy \(G\)-distributed sequences low-discrepancy sequences quasi-Monte Carlo integration |
| url | https://ictp.acad.ro/jnaat/journal/article/view/847 |
| work_keys_str_mv | AT nataliarosca generationofnonuniformlowdiscrepancysequencesinthemultidimensionalcase |