Preconditioning techniques for large linear systems: a survey

By Michele Benzi. 2002

1,411 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/6c15b76f9018e24cbb16909a9d77df24da948ab9

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In Atomic and Molecular Physics, and Optics

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems Part I - System overview and formulation (2011, background): “It is beyond the scope of this paper to discuss the required properties of preconditioners, but there are many excellent treatises on the subject (e.g. Golub and van Loan, 1989; Benzi, 2002; Tshimanga, 2007; Tshimanga et al., 2008).”
Recent computational developments in Krylov subspace methods for linear systems (2007, background): “Again, we refer to [26], [32], [54], [68], [273], and references therein for details.”
On iterative methods for the incompressible Stokes problem (2011, neutral): “Many iterative methods have been proposed for these problems, see for example [2–7].”
divand-1.0: n -dimensional variational data analysis for ocean observations (2013, methodology): “In this case, the matrixPinv can also be decomposed using a modified incomplete Cholesky decomposition (Jones and Plassmann, 1995; Benzi, 2002).”
Scaling up Natural Gradient by Sparsely Factorizing the Inverse Fisher Matrix (2015, methodology): “The incomplete Cholesky factorization (Meijerink & van der Vorst, 1977; Benzi, 2002) computes an approximate factorization A ≈ LLT where the lower triangular factor L shares the sparsity structure of A.”
A black-box rational Arnoldi variant for Cauchy–Stieltjes matrix functions (2013, background): “vation may be the stronger diagonal dominance of systems with larger shifts, which renders the ILU(0) preconditioner to be more effective, a well-known effect [9].”
The physics of streamer discharge phenomena (2020, methodology): “However, when used in combination with a suitable preconditioner [298], large sparse systems can be solved efficiently.”
Limited‐memory preconditioners, with application to incremental four‐dimensional variational data assimilation (2008, background): “It is widely recognized that there is no universal way to design a preconditioner for all types of problems (Benzi, 2002).”
Performance of fully coupled domain decomposition preconditioners for finite element transport/reaction simulations (2005, methodology): “[7,11,12,13,28]). The choices also include the selection of subdomain solver such as an incomplete LU factorization (ILU) (with further options for dropping nonzeros in the factorizations and ordering equations within a subdomain [ 1 ] ), and the introduction of a coarse grid solve [10,37].”
Iterative Krylov Methods for Large Linear Systems (2003, methodology): “For a good overview on the SPAI techniques see [22].”
Neurobiology of Aging: Contents (2005, positive): “…in the solution of linear systems arising from the discretization of scalar partial differential equations of elliptic type, and is widely used in many areas of computational science and engineering; see Benzi (2002), Meurant (1999), Saad (2003), van der Vorst (2003) for recent treatments.”
Jacobian-free Newton-Krylov methods: a survey of approaches and applications (2004, methodology): “We refer to [11,13,84,157] for more details on Krylov methods, and for preconditioning for linear problems.”
An Inexact Cayley Transform Method For Inverse Eigenvalue Problems (2004, background): “But since the Jacobian matrices (see (7) and (11)) are in general nonsymmetric and dense, how to choose a good preconditioner needs a further study, see for instance a survey paper [4].”
A Survey of Optimization Methods From a Machine Learning Perspective (2019, background): “preconditioner is obviously structured, or sparse, it will be beneficial to the calculation [123].”
The Jacobi–Davidson method (2006, methodology): “, [6, 56] for a recent review of modern preconditioning techniques.”
MINRES-QLP: A Krylov Subspace Method for Indefinite or Singular Symmetric Systems (2010, background): “For a comprehensive survey of preconditioning techniques, see Benzi [3].”