# Revisiting Performance of BiCGStab Methods for Solving Systems with Multiple Right-Hand Sides

## TL;DR

This paper evaluates the performance of BiCGStab and its variants for solving large sparse linear systems with multiple right-hand sides, proposing an analytical model and optimization techniques that enhance efficiency by reducing memory traffic.

## Contribution

The paper introduces an analytical execution time model for BiCGStab variants and proposes merging vector operations to improve performance in multi-RHS systems.

## Key findings

- Vector operation merging reduces memory traffic by about 30%.
- BiCGStab variants' applicability depends on system characteristics.
- Analytical model aligns well with numerical experiments.

## Abstract

The paper discusses the efficiency of the classical BiCGStab method and several of its modifications for solving systems with multiple right-hand side vectors. These iterative methods are widely used for solving systems with large sparse matrices. The paper presents execution time analytical model for the time to solve the systems. The BiCGStab method and several modifications including the Reordered BiCGStab and Pipelined BiCGStab methods are analyzed and the range of applicability for each method providing the best execution time is highlighted. The results of the analytical model are validated by the numerical experiments and compared with results of other authors. The presented results demonstrate an increasing role of the vector operations when performing simulations with multiple right-hand side vectors. The proposed merging of vector operations allows to reduce the memory traffic and improve performance of the calculations by about 30%.