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Improving GMRES( m ) using an adaptive switching controller
Author(s) -
Cabral Juan C.,
Schaerer Christian E.,
Bhaya Amit
Publication year - 2020
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2305
Subject(s) - generalized minimal residual method , krylov subspace , mathematics , convergence (economics) , residual , subspace topology , dimension (graph theory) , controller (irrigation) , rate of convergence , linear system , control theory (sociology) , mathematical optimization , iterative method , algorithm , computer science , control (management) , mathematical analysis , pure mathematics , key (lock) , computer security , artificial intelligence , agronomy , economics , biology , economic growth
Summary The restarted generalized minimal residual (denoted as GMRES( m )) normally used for solving a linear system of equations of the form Ax = b has the drawback of eventually presenting a stagnation or a slowdown in its rate of convergence at certain restarting cycles. In this article, a switching controller is introduced to modify the structure of the GMRES( m ) when a stagnation is detected, enlarging and enriching the subspace. In addition, an adaptive control law is introduced to update the restarting parameter to modify the dimension of the Krylov subspace. This combination of strategies is competitive from the point of view of helping to avoid the stagnation and accelerating the convergence with respect to the number of iterations and the computational time. Computational experiments corroborate the theoretical results.