منابع مشابه
Hierarchical Krylov and nested Krylov methods for extreme-scale computing
The solution of large, sparse linear systems is often a dominant phase of computation for simulations based on partial differential equations, which are ubiquitous in scientific and engineering applications. While preconditioned Krylov methods are widely used and offer many advantages for solving sparse linear systems that do not have highly convergent, geometric multigrid solvers or specialize...
متن کاملRelaxation strategies for nested Krylov methods
There are classes of linear problems for which the matrix-vector product is a time consuming operation because an expensive approximation method is required to compute it to a given accuracy. In recent years different authors have investigated the use of, what is called, relaxation strategies for various Krylov subspace methods. These relaxation strategies aim to minimize the amount of work tha...
متن کاملNested Krylov Methods and Preserving the Orthogonality
SUMMARY Recently the GMRESR inner-outer iteration scheme for the solution of linear systems of equations has been proposed by Van der Vorst and Vuik. Similar methods have been proposed by Axelsson and Vassilevski 1] and Saad (FGMRES) 10]. The outer iteration is GCR, which minimizes the residual over a given set of direction vectors. The inner iteration is GMRES, which at each step computes a ne...
متن کاملNested Krylov Methods for Shifted Linear Systems
and {ωk}k=1 ∈ C is a sequence of n distinct shifts. For example, shifted linear systems arise in model order reduction as well as in the geophysical exploration of both acoustic and elastic waves. In our application, we focus on wave propagation through elastic media in a frequency-domain formulation. This formulation has specific advantages when modeling visco-elastic effects. In order to impr...
متن کاملIterative Methods Based on Krylov Subspaces
with a symmetric and positive definite operator A defined on a Hilbert space V with dimV = N and its preconditioned version PCG. We derive the CG from the projection in A-inner product point of view. We shall use (·, ·) for the standard inner product and (·, ·)A for the inner product introduced by the SPD operator A. When we say ‘orthogonal’ vectors, we refer to the default (·, ·) inner product...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1996
ISSN: 0377-0427
DOI: 10.1016/0377-0427(94)00123-5