A parallel cyclic reduction algorithm for pentadiagonal systems with application to a convection-dominated heston pde

Abstract

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. © 2021 Society for Industrial and Applied Mathematics Publications. All rights reserved.