Abstract
In this paper, a kind of modified GMRES(m) algorithm is proposed and its convergence theory is well established. By properly varying the restart parameter m in the GMRES(m) algorithm, the computational efficiency and precision can be significantly improved. Because the parameter m can be very small, the storage and computations are greatly saved. In addition, the new algorithm is successfully used to solve a heat conduction problem and a Laplace equation problem. Numerical results show that it is not only highly effective and accurate, but also can avoid slow convergence or failure behaviour of the GMRES(m) algorithm. The superiorities will be much more remarkable for the solution of large scale problems. So it has extensive prospect in scientific computing and engineering applications.
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