CAJ | 학술논문

求解一般矩阵特征值问题的第一步即进行Hessenberg约化。给出了矩阵的Hessenberg约化算法在GPU上实现的具体方案。针对CPU－GPU混合系统，对基于块计算的Hessenberg约化算法进行了计算任务的划分，并通过详细分析每次循环时各任务的计算量，设计了一种较为合理的分阶段混合调度策略。数值实验表明，使用CPU－GPU混合调度的方案相比直接使用CUBLAS库方案平均获得了约47％的性能提升，而且相比使用CPU上标准的BLAS库函数最高获得了超过7倍的加速比。
구해일반구진특정치문제적제일보즉진행Hessenberg약화。급출료구진적Hessenberg약화산법재GPU상실현적구체방안。침대CPU－GPU혼합계통，대기우괴계산적Hessenberg약화산법진행료계산임무적화분，병통과상세분석매차순배시각임무적계산량，설계료일충교위합리적분계단혼합조도책략。수치실험표명，사용CPU－GPU혼합조도적방안상비직접사용CUBLAS고방안평균획득료약47％적성능제승，이차상비사용CPU상표준적BLAS고함수최고획득료초과7배적가속비。
The first step of solving the eigenvalue problem of a nonsymmetric matirx is to reduce the matrix to an upper Hessenberg form .A concretely plan is designed for the reduction of a matrix on GPU .For the CPU-GPU hy-brid system, The whole work of the block hessenberg reduction algorithm is split into several tasks .The computa-tional complexity of each task in each loop is analyzed , and then a more reasonable scheduling strategy is presen-ted.The numerical experiment shows that the algorithm using the hybrid scheduling plan presented acquires about 47 percentage of performance improvement compared with the orginal transplant plan using CUBLAS only in aver -age.Also it achieves a speedup of more than 7 times than that of the current BLAS library .