BLOCK KRYLOV SPACE METHODS FOR LINEAR SYSTEMS WITHGutknecht, Martin HFebruary, Version O F
(1990),pp.656–694.KelleyKrylovMethodsKrylovMethodsOverviewGMRESConjugateGradientIterationOtherKrylovMethodsPreconditioningExercisesKrylovMethodsKryloviterativemethodsobtaintheorydoresidualfunctionoveraffinespaceinitialiteratekthKrylovsubspaceKelleyKrylovMethodsKrylovMethodsOverviewGMRESConjugateGradientIterationOtherKrylovMethods...
Krylov subspace methods – p. 2 Projection methods for large-scale problems Given the system of n equations F(x) = 0 x ∈ R n - Construct approximation space K m (m = dim(K m ) ) - Find x ∈ K m such that x ≈ x Projection onto a much smaller space m n Approximation process...
These methods are designed to efficiently compute approximate solutions to largelinear systems by iteratively building a subspace of the Krylov space generated by the matrix. 一种分类Krylov子空间方法的方法是基于使用的矩阵-向量乘法的类型。例如,共轭梯度法是一种Krylov子空间方法,它使用对称正定矩阵,而广义...
Chapters 3-5 provide the conjugate gradient algorithm after a more general discussion of Krylov space methods. Here we have already a clear deviation from the standard introduction of the cg methods. Usually the discussion is based on the three-term recurrence relations for the vectors, while the...
We study stopping criteria that are suitable in the solution by Krylov space based methods of linear and non linear systems of equations arising from the m... M Arioli,D Loghin - 《Electronic Transactions on Numerical Analysis Etna》 被引量: 45发表: 2007年 Approximation of matrix operators app...
The introduction of the low-rank truncations that lead to (5.6) implies that the constraints imposed on the residual vector are no longer in terms of the space spanned by Zm and the results presented in Proposition 3.1 with [Math Processing Error]Wm=AZm−[vec(E1),…,vec(Em)] hold. ...
(PDEs) or systems of PDEs. The main components of the package are standard Krylov methods, algebraic multigrid methods, and incomplete factorization methods. Based on these standard techniques, we build efficient solvers, based on the framework of Auxiliary Space Preconditioning, for several ...
We will see in section 3.4 that if we want to obtain good accuracy, then the size of the Krylov space m has to be large when ‖τA˜‖ is large. This is worrying because it may indicate that an impractical amount of memory storage and computational cost could be necessary to obtain ...
In this paper we restrict ourselves to the one-block case and two space dimensions. For the space discretization we use finite volumes and a staggered grid. For the time discretization we use the Euler Backward finite difference scheme tog... 展开 ...