Clock Math — a System for Solving SLEs Exactly

Autor:	Jakub Hladík, Róbert Lórencz, Ivan Šimeček
Jazyk:	angličtina
Rok vydání:	2013
Předmět:	integer arithmetic modular arithmetic Hilbert’s matrix error-free GPGPU solver OpenCL optimizations. Engineering (General). Civil engineering (General) TA1-2040
Zdroj:	Acta Polytechnica, Vol 53, Iss 2 (2013)
Druh dokumentu:	article
ISSN:	1210-2709 1805-2363
Popis:	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.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/425cbe3e525242bbbf2cb1e386dc195d Zobrazit plný text záznamu View record in DOAJ