@Article{JICS-1-303, author = {}, title = {Product Hybrid Block GMRES for Nonsymmetrical Linear Systems with Multiple Right-hand Sides}, journal = {Journal of Information and Computing Science}, year = {2024}, volume = {1}, number = {5}, pages = {303--310}, abstract = {Recently, the complementary behavior of restarted GMRES has been studied. We observed that successive cycles of restarted block BGMRES (BGMRES(m,s)) can also complement one another harmoniously in reducing the iterative residual. In the present paper, this characterization of BGMRES(m,s) is exploited to form a hybrid block iterative scheme. In particular, a product hybrid block GMRES algorithm for nonsymmetrical systems with multiple right-hand sides is proposed. The new algorithm combines the advantage of Simoncini’s Hybrid Block GMRES and Zhong’s Product Hybrid GMRES. Numerical experiments are conducted to show that the new algorithm can offer significant improvement over the hybrid block GMRES. }, issn = {1746-7659}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jics/22829.html} }