Acta Polytechnica | 卷:53 |
Clock Math — a System for Solving SLEs Exactly | |
关键词: integer arithmetic; modular arithmetic; Hilbert’s matrix; error-free; GPGPU; solver; OpenCL; optimizations.; | |
DOI : | |
来源: DOAJ |
【 摘 要 】
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.
【 授权许可】
Unknown