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math.NA2026
Neural Network Preconditioning: A Case Study for the Solution of the Parametric Helmholtz Equation
Luc Giraud, Carola Kruse, Paul Mycek +2
This work presents a hybrid numerical approach for solving linear systems arising from the discretization of the two-dimensional parametric Helmholtz equation. A convolutional neur…
math.NA2016
Analyzing the effect of local rounding error propagation on the maximal attainable accuracy of the pipelined Conjugate Gradient method
Siegfried Cools, Emrullah Fatih Yetkin, Emmanuel Agullo +2
Pipelined Krylov subspace methods typically offer improved strong scaling on parallel HPC hardware compared to standard Krylov subspace methods for large and sparse linear systems.…
math.NA2013
Deflation and augmentation techniques in Krylov subspace methods for the solution of linear systems
Olivier Coulaud, Luc Giraud, Pierre Ramet +1
In this paper we present deflation and augmentation techniques that have been designed to accelerate the convergence of Krylov subspace methods for the solution of linear systems o…