A direct tridiagonal solver based on Givens rotations for GPU architectures

作者：Venetis I E^*; Kouris A; Sobczyk A; Gallopoulos E; Sameh A H

来源：Parallel Computing, 2015, 49: 101-116.

DOI：10.1016/j.parco.2015.03.008

• Parallel tridiagonal solvers
• Givens rotations-based QR
• GPU
• Spike framework
• Singular matrix
• Low-rank modification

g-Spike, a parallel algorithm for solving general nonsymmetric tridiagonal systems for the GPU, and its CUDA implementation are described. The solver is based on the Spike framework, applying Givens rotations and QR factorization without pivoting. It also implements a low-rank modification strategy to compute the Spike DS decomposition even when the partitioning defines singular submatrices along the diagonal. The method is also used to solve the reduced system resulting from the Spike partitioning. Numerical experiments with problems of high order indicate that g-Spike is competitive in runtime with existing GPU methods, and can provide acceptable results when other methods cannot be applied or fail.

• 出版日期2015-11