A Preconditioner for Generalized Saddle Point Problems

By Michele Benzi, Gene H. Golub. SIAM Journal on Matrix Analysis and Applications, 2004

467 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/38871afeb038c03d68d49ced6c8e270b26073aa8

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In Atomic and Molecular Physics, and Optics

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

A Generalized Preconditioned MHSS Method for a Class of Complex Symmetric Linear Systems (2013, methodology): “The method was extended to the solution of saddle point problems [12,13] and the idea of using two parameters to accelerate the HSS iteration method for solving saddle point linear systems was introduced in [6] and deeply discussed in [3].”
Block preconditioning of real-valued iterative algorithms for complex linear systems (2007, background): “Also, the result on the spectral radius remains valid under the assumptions that A is positive semidefinite and B nonsingular (Benzi & Golub, 2004).”
A Relaxed HSS Preconditioner for Saddle Point Problems from Meshfree Discretization (2013, methodology): “For saddle point problems arising from the EFG method, the class of preconditioners we considered in this paper is a class of HSS preconditioners, which was proposed by Benzi and Golub in [13].”
A dimensional split preconditioner for Stokes and linearized Navier-Stokes equations (2011, background): “Incidentally, it was noted in [4] that diagonal scaling is very beneficial for the HSS preconditioner as well.”
Neurobiology of Aging: Contents (2005, unknown): “The method can be made to converge even when H is positive semidefinite and singular, provided that ker(H)∩ker(B) = {0}; see Benzi and Golub (2004).”
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems (2002, methodology): “Recently, the preconditioned HSS iterations and the extension of the HSS method to positive definite and positive semidefinite linear systems have been studied in [6,10,4,11,13,8,3].”
Regularized HSS iteration methods for saddle-point linear systems (2017, methodology): “As the matrix Ẽ(α) is of full column rank, from [9] we straightforwardly know that ρ(Ľ(α)) < 1.”
Linear Lower Bounds and Conditioning of Differentiable Games (2019, methodology): “In fact, several techniques to precondition systems of linear equation make use of casting the SLE as a game and optimising it with proximal methods, such as Benzi and Golub (2004).”