Parallelism and Iterative bi-Lanczos Solvers

The paper provides an overview of the amenability of applying modern parallel-programming techniques in order to improve the performance of iterative solvers for systems of linear equations. Various conveniences, but also potential obstacles, are listed and described by analysing a popular iterative solver based on Lanczos biorthogonalisation, Bi-Conjugate Gradient Stabilised (BiCGStab). Even though a developer may stumble upon different characteristics and restrictions of modern multi/many-core hardware, the performance of iterative methods is greatly improved even by applying naive data-parallel techniques on existing algorithms. Moreover, by using a proper data layout, merging operations and avoiding unnecessary communication and memory latencies, one can achieve major performance improvements for large-scale problems.