Recently, communication-avoiding methods have been developed to reduce the communication overheads in Krylov subspace iterative solvers. On modern computer architectures, communications between processors are much slower than floating-point arithmetic operations on a given processor. Communication-avoiding techniques reduce either communications between processors or data movements between levels of the memory hierarchy, by reformulating the communication-bound kernels (more frequently SpMV kernels) and the orthogonalization operations within the Krylov iterative solver. Different works have studied the communication-avoiding methods for multicore processors and multi-GPU machines~\cite{}.
+Compared to all these works, the originality of our work is to build a second
+iteration over a Krylov iterative method and to minimize the residuals with a
+least-squares method after a given number of outer iteration.
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