A safeguard approach to detect stagnation of GMRES(m) with applications in Newton-Krylov methods

Gomes-Ruggiero, Márcia A.; Lopes, Véra Lucia Rocha; Toledo-Benavides, Julia Victoria

doi:10.1590/s0101-82052008000200004

Cited by 4 publications

(2 citation statements)

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“…The strategy behind the techniques for avoiding stagnation rely on modifying the search subspace. Some alternatives are to modify the initial vector that is usually the last residual vector, 7,11,23,24 to include other information or a combination of strategies 5,9,25,26 . In the following section, the three parts that form the controller are introduced.…”

Section: Adaptive Switching Controllermentioning

confidence: 99%

“…The latter means that the new subspace generated is close to the previous one so that the approximation does not make any progress 4 . The problem of improving the rate of convergence and avoiding stagnation has been addressed using several strategies; see, for instance, References 5‐12 and the references therein. In this article, two strategies are used to ensure that the residual has monotonically decreasing behavior.…”

Section: Introductionmentioning

confidence: 99%

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Improving GMRES(m) using an adaptive switching controller

Cabral

Schaerer

Bhaya

2020

Numerical Linear Algebra App

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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.

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Section: Adaptive Switching Controllermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%