SIAM Journal on Scientific Computing, Volume 43, Issue 2, Page C177-C202, January 2021.
Based on the parallel cyclic reduction technique, a promising new parallel algorithm is designed for pentadiagonal systems. Subject to fulfilling stability conditions, this highly parallelizable algorithm works very well for systems of any size. The solver is implemented on a graphics processing unit using the CUDA programming platform where it is empirically studied for its performance in comparison with some of the present-day prominent parallel solvers. The construction of the new algorithm is originally motivated by a real-world application in computational finance. Accordingly, it is employed successfully to numerically solve the convection-dominated Heston partial differential equation for pricing a financial option, and implementation of the full solver is discussed in detail.

中文翻译：

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五角对角系统的并行循环约简算法及其在对流主导的Heston PDE中的应用

SIAM科学计算杂志，第43卷，第2期，第C177-C202页，2021年1月。
基于并行循环约简技术，为五对角系统设计了一种很有前途的新并行算法。在满足稳定条件的前提下，这种高度可并行化的算法非常适合任何规模的系统。该解算器是使用CUDA编程平台在图形处理单元上实现的，与目前一些著名的并行解算器相比，对它的性能进行了经验研究。新算法的构建最初是由计算金融中的实际应用推动的。因此，成功地将其用于对流占优势的Heston偏微分方程进行数值求解以对金融期权定价，并详细讨论了全求解器的实现。