Iterative Krylov Methods for Large Linear Systems

By Henk A. van der Vorst. 2003

920 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/ebd0b878599f41187ab5d5f4719ed2ecefd21f0d

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In Computational Theory and Mathematics

Citations in the corpus

Linear Algebra and its Applications (2010, neutral): “…of (3.10) then reads with the straightforward definition of ˜ r u , ˜ r v and CG is a natural choice as it optimal in the following sense [48]: for any initial guess ˜ v 0 it computes iterants ˜ v i which satisfy the polynomial relation 1 ˜ v i − ˜ v = P i ( (cid:11) M )( ˜ v 0 − ˜ v )…”
The Matrix Exponential (2015, neutral): “[17, 39, 46]).”
Computing procedures for genetic evaluation including phenotypic, full pedigree, and genomic information. (2009, background): “The standard way in conjugate-gradient types of algorithms to improve convergence is by choice of a preconditioner M , which approximates LHS but is easily invertible (Van der Vorst, 2003).”
Modified HSS iteration methods for a class of complex symmetric linear systems (2010, positive): “This necessitates the use of complex arithmetic, and the iterate x (k+1) in the second-half step may be computed either exactly by some variant of Bunch–Parlett factorization or inexactly by certain Krylov subspace iteration schemes such as the Concus–Golub–Widlund (CGW) method or GMRES; see [10,13,”
Advances in Iterative Methods and Preconditioners for the Helmholtz Equation (2008, methodology): “The idea of Krylov subspace methods can be outlined as follows [63, 105, 127].”
Shaping regularization in geophysical-estimation problems (2007, positive): “Manuscript received by the Editor April 7, 2006; revised manuscript received September 13, 2006; published online February 15, 2007. are represented by sparse matrices and can be computed efficiently ͑Saad, 2003; van der Vorst, 2003͒.”
An accurate conservative level set/ghost fluid method for simulating turbulent atomization (2008, methodology): “This variable-coefficient, elliptic equation is solved using a combination of Krylov-based methods [27] preconditioned using a multi-grid solver [28].”
High order conservative finite difference scheme for variable density low Mach number turbulent flows (2007, methodology): “The pressure Poisson equation is then solved to enforce continuity using a combination of spectral methods, Krylov-based methods [25], and multi-grid methods [26], depending on the geometry of the problem.”
Recent computational developments in Krylov subspace methods for linear systems (2007, methodology): “GCG uses orthogonal directions z i , i = 1, . . . , m, (with respect to a particular inner product) to span a subspace in which the approximate solution x m is taken so that the residual norm is minimized (in some norm induced by some -possibly different -inner product); see Axelsson [12] It turns o”