We present a dynamically adjusted deflated restarting procedure for the Generalized Conjugate Residual method with inner Orthogonalization (GCRO). The proposed method employs a GCR solver for the outer iteration and t...
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ISBN:
(数字)9781624105890
ISBN:
(纸本)9781624105890
We present a dynamically adjusted deflated restarting procedure for the Generalized Conjugate Residual method with inner Orthogonalization (GCRO). The proposed method employs a GCR solver for the outer iteration and the generalized minimal residual (GMRES) with deflated restarting in the inner iteration. Approximate eigenpairs are evaluated at the end of each inner GMRES restart cycle. Our approach determines the number of vectors to be deflated from the spectrum based on the number of negative Ritz values, k*. We show that the approach restores convergence to cases where GMRES with restart failed and compare the approach against standard GMRES with restarts and deflated restarting. Efficiency is demonstrated for a two-dimensional NACA 0012 airfoil and a three-dimensional Common Research Model (CRM) wing. In addition, numerical experiments confirm the scalability of the solver.
We consider a one-dimensional bisection method for finding the zero of a function, where function evaluations can be performed asynchronously in a parallel computing environment. Using dynamic programming, we characte...
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ISBN:
(纸本)9781479974863
We consider a one-dimensional bisection method for finding the zero of a function, where function evaluations can be performed asynchronously in a parallel computing environment. Using dynamic programming, we characterize the Bayes-optimal policy for sequentially choosing points at which to query the function. In choosing these points, we face a trade-off between aggressively reducing the search space in the short term, and maintaining a desirable spread of queries in the long-term. Our results provide insight on how this trade-off is affected by function evaluation times, risk preferences, and computational budget.
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