Adaptive System Identification for GMRES(m) Based on DMDc
Abstract
The Restarted Generalized Minimal Residual Method (GMRES(m)) is a widely used iterative solver for large-scale, sparse, and nonsymmetric linear systems [4]. However, its convergence is not guaranteed [1]. To improve convergence, the restart parameter m must be properly tuned; however, there is currently no general rule for selecting its optimal value. The primary challenge in designing a rule is the internal nonlinear dynamics of GMRES(m), which is well understood in its construction, but less well understood in its behavior. In this work, we design a system identification model (SIM) to address the challenge of capturing the internal nonlinear behavior of GMRES(m). The results show the efficiency of the SIM as an observer of the internal dynamics. Future works will be oriented towards using the SIM to enhance the convergence of the method. [...]
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References
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