A Framework for Deflated and Augmented Krylov Subspace Methods
نویسندگان
چکیده
منابع مشابه
A Framework for Deflated and Augmented Krylov Subspace Methods
We consider deflation and augmentation techniques for accelerating the convergence of Krylov subspace methods for the solution of nonsingular linear algebraic systems. Despite some formal similarity, the two techniques are conceptually different from preconditioning. Deflation (in the sense the term is used here) “removes” certain parts from the operator making it singular, while augmentation a...
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We present an extension of the framework of Gaul et al. (SIAM J. Matrix Anal. Appl. 34, 495–518 (2013)) for deflated and augmented Krylov subspace methods satisfying a Galerkin condition to more general Petrov–Galerkin conditions. The main goal is to apply the framework to the biconjugate gradient method (BiCG) and some of its generalizations, including BiCGStab and IDR(s). For such application...
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We present a general framework for a number of techniques based on projection methods onàugmented Krylov subspaces'. These methods include the deeated GM-RES algorithm, an inner-outer FGMRES iteration algorithm, and the class of block Krylov methods. Augmented Krylov subspace methods often show a signiicant improvement in convergence rate when compared with their standard counterparts using the...
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The balancing Neumann-Neumann (BNN) and the additive coarse grid correction (BPS) preconditioner are fast and successful preconditioners within domain decomposition methods for solving partial differential equations. For certain elliptic problems these preconditioners lead to condition numbers which are independent of the mesh sizes and are independent of jumps in the coefficients (BNN). Here w...
متن کاملAnalysis of Augmented Krylov Subspace Methods
Residual norm estimates are derived for a general class of methods based on projection techniques on subspaces of the form K m + W, where K m is the standard Krylov subspace associated with the original linear system, and W is some other subspace. Thesèaugmented Krylov subspace methods' include eigenvalue deeation techniques as well as block-Krylov methods. Residual bounds are established which...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2013
ISSN: 0895-4798,1095-7162
DOI: 10.1137/110820713