Clock Math — a System for Solving SLEs Exactly

Acta Polytechnica

Jakub Hladík¹  Róbert Lórencz¹  Ivan Šimeček¹ 

关键词: integer arithmetic;    modular arithmetic;    Hilbert’s matrix;    error-free;    GPGPU;    solver;    OpenCL;    optimizations.;   

DOI  :  

来源: Czech Technical University in Prague, Faculty of M

【 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