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Analysis of an Implicitly Restarted Simpler GMRES Variant of Augmented GMRES
2010We analyze a Simpler GMRES variant of augmented GMRES with implicit restarting for solving nonsymmetric linear systems with small eigenvalues. The use of a shifted Arnoldi process in the Simpler GMRES variant for computing Arnoldi basis vectors has the advantage of not requiring an upper Hessenberg factorization and this often leads to cheaper ...
Ravindra Boojhawon +3 more
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GPU-Accelerated Preconditioned GMRES Solver
2016 IEEE 2nd International Conference on Big Data Security on Cloud (BigDataSecurity), IEEE International Conference on High Performance and Smart Computing (HPSC), and IEEE International Conference on Intelligent Data and Security (IDS), 2016Linear solvers and parallel computing are crucial for developing a new generation reservoir simulator. To acquire satisfied acceleration performance, we study the parallel algorithms of linear solvers with preconditioners on GPUs (Graphics Processing Units).
Bo Yang +3 more
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Applied Mathematics and Computation, 1997
The GMRES method for a nonsymmetric linear system arizing from discretization of a general second-order elliptic boundary value problem is preconditioned by a multigrid iteration on the whole system. It is proved that the preconditioned system is nonsymmetric positive definite for sufficiently small coarsest mesh.
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The GMRES method for a nonsymmetric linear system arizing from discretization of a general second-order elliptic boundary value problem is preconditioned by a multigrid iteration on the whole system. It is proved that the preconditioned system is nonsymmetric positive definite for sufficiently small coarsest mesh.
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Shifted GMRES for oscillatory integrals
Numerische Mathematik, 2009By applying the generalized minimal residual (GMRES) algorithm to a shifted linear differential operator, the author constructs a new method for approximating the oscillatory integral \(\int_a^b f(x)e^{i\omega g(x)}dx\). Unlike the existing methods, this one satisfies simultaneously the following properties: it has high asymptotic order and stability ...
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Große dünn besetzte lineare Gleichungssysteme sind zentral für viele komplexe und rechenintensive Probleme in verschiedenen wissenschaftlichen Bereichen. Hochleistungsrechnen (High Performance Computing, HPC) und hochgradig parallelisierbare iterative Verfahren sind wichtige Werkzeuge, um diese Systeme effizient zu lösen.
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Verfahren der konjugierten Gradienten und GMRES-Verfahren
2000Ziel der nachfolgenden Betrachtungen ist erneut die approximative Losung eines regularen linearen Gleichungssystems $$Ax = b\quad (A \in {\mathbb{R}^{N \times N}}\;regul\ddot ar,\quad b \in {\mathbb{R}^N})$$ (mit der eindeutigen Losung x * = A −1 b ∈ℝ N ), und hierzu seien $$\{ 0\} \subset {D_1} \subset {D_2} \subset ...
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Comparing GMRES and P-GMRES in domain decomposition with approximate subdomain solution
2000Electrical Engineering, Mathematics and Computer ...
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