dorsal/arxiv
View SchemaAlmost Optimal Solution of Initial-Value Problems by Randomized and Quantum Algorithms
| Authors | Boleslaw Kacewicz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510045 |
| URL | https://arxiv.org/abs/quant-ph/0510045 |
| Journal | Journal of Complexity 22 (2006), 676-690 |
Abstract
We establish essentially optimal bounds on the complexity of initial-value problems in the randomized and quantum settings. For this purpose we define a sequence of new algorithms whose error/cost properties improve from step to step. These algorithms yield new upper complexity bounds, which differ from known lower bounds by only an arbitrarily small positive parameter in the exponent, and a logarithmic factor. In both the randomized and quantum settings, initial-value problems turn out to be essentially as difficult as scalar integration.
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"abstract": "We establish essentially optimal bounds on the complexity of initial-value\nproblems in the randomized and quantum settings. For this purpose we define a\nsequence of new algorithms whose error/cost properties improve from step to\nstep. These algorithms yield new upper complexity bounds, which differ from\nknown lower bounds by only an arbitrarily small positive parameter in the\nexponent, and a logarithmic factor. In both the randomized and quantum\nsettings, initial-value problems turn out to be essentially as difficult as\nscalar integration.",
"arxiv_id": "quant-ph/0510045",
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"Boleslaw Kacewicz"
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"journal_ref": "Journal of Complexity 22 (2006), 676-690",
"title": "Almost Optimal Solution of Initial-Value Problems by Randomized and Quantum Algorithms",
"url": "https://arxiv.org/abs/quant-ph/0510045"
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