Accelerated GCRO-DR method for solving sequences of systems of linear equations

By recycling some error approximations generated during a previous cycle of iterations, we present a technique for improving the convergence of GCRO-DR. The scheme is able to mitigate the occurrence of small skip angles occurring in GCRO-DR, and thus considerably accelerates the convergence. The alternative phenomenon of the residual vectors is examined numerically, and the effectiveness of the new method is illustrated by several examples from practical applications.