Clock Math — a System for Solving SLEs Exactly
dc.contributor.author | Hladík , Jakub | |
dc.contributor.author | Lórencz , Róbert | |
dc.contributor.author | Šimeček , Ivan | |
dc.date.accessioned | 2017-02-09T08:07:00Z | |
dc.date.available | 2017-02-09T08:07:00Z | |
dc.date.issued | 2013 | |
dc.identifier.citation | Acta Polytechnica. 2013, vol. 53, no. 2. | |
dc.identifier.issn | 1210-2709 (print) | |
dc.identifier.issn | 1805-2363 (online) | |
dc.identifier.uri | http://hdl.handle.net/10467/67054 | |
dc.description.abstract | In this paper, we present a GPU-accelerated hybrid system that solves ill-conditioned systems of linear equations exactly. Exactly means without rounding errors due to using integer arithmetics. First, we scale floating-point numbers up to integers, then we solve dozens of SLEs within different modular arithmetics and then we assemble sub-solutions back using the Chinese remainder theorem. This approach effectively bypasses current CPU floating-point limitations. The system is capable of solving Hilbert’s matrix without losing a single bit of precision, and with a significant speedup compared to existing CPU solvers. | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | eng | |
dc.publisher | České vysoké učení technické v Praze | cs |
dc.publisher | Czech Technical University in Prague | en |
dc.relation.ispartofseries | Acta Polytechnica | |
dc.relation.uri | https://ojs.cvut.cz/ojs/index.php/ap/article/view/1795 | |
dc.rights | Creative Commons Attribution 4.0 International License | en |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
dc.subject | integer arithmetic | en |
dc.subject | modular arithmetic | en |
dc.subject | Hilbert’s matrix | en |
dc.subject | error-free | en |
dc.subject | GPGPU | en |
dc.subject | solver | en |
dc.subject | OpenCL | en |
dc.subject | optimizations. | en |
dc.title | Clock Math — a System for Solving SLEs Exactly | |
dc.type | article | en |
dc.date.updated | 2017-02-09T08:07:00Z | |
dc.rights.access | openAccess | |
dc.type.status | Peer-reviewed | |
dc.type.version | publishedVersion |
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