  Recently, a new variant of the BiCGStab method, known as the pipeline
BiCGStab, has been proposed. This method can achieve a higher degree of
scalability and speed-up rates through a mechanism in which the communication
phase for the computation of the inner product can be overlapped with the
computation of the matrix-vector product. On the other hand, there exist
several generalized iteration methods with better convergence behavior than
BiCGStab such as ssBiCGSafe, BiCGSafe, GPBi-CG. Of these methods, ssBiCGSafe,
which requires a single phase of computing inner products per one iteration, is
best suited for high-performance computing systems. In this paper, inspired by
the success of the pipelined BiCGStab method, we propose variations of the
ssBiCGSafe method, in which only one phase of inner product computation per
iteration is required and this inner product computation phase can be
overlapped with the matrix-vector computation. Through numerical experiments,
we show that the proposed methods lead to improvements in convergence behavior
and execution time compared to the pipelined BiCGStab and ssBiCGSafe methods.

Distributed, Parallel, and Cluster Computing;Mathematical Software