A Technique for Accelerating the Convergence of Restarted GMRES
Allison H. Baker, Elizabeth R. Jessup, Thomas A. Manteuffel · SIAM Journal on Matrix Analysis and Applications · 2005
We have observed that the residual vectors at the end of each restart cycle of restarted GMRES often alternate direction in a cyclic fashion, thereby slowing convergence. We present a new technique for accelerating the convergence of restarted GMRES by disrupting this alternating pattern. The new algorithm resembles a full conjugate gradient method with polynomial preconditioning, and its implementation requires minimal changes to the standard restarted GMRES algorithm.