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A modified ASOR-like method for augmented linear systems
For solving an augmented linear system, Njeru and Guo presented an accelerated SOR-like (ASOR) method in (P. N. Njeru and X.-P. Guo. Accelerated...
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Circulant preconditioners for a kind of spatial fractional diffusion equations
In this paper, circulant preconditioners are studied for discretized matrices arising from finite difference schemes for a kind of spatial fractional...
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Circulant preconditioners for analytic functions of Toeplitz matrices
Circulant preconditioning for symmetric Toeplitz systems has been well developed over the past few decades. For a large class of such systems,...
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Backward step control for Hilbert space problems
We analyze backward step control globalization for finding zeros of Gâteaux-differentiable functions that map from a Banach space to a Hilbert space....
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On the eigenvalues of the saddle point matrices discretized from Navier–Stokes equations
In this paper, we study the spectral distributions of the saddle point matrices arising from the discretization and linearization of the...
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A supernodal block factorized sparse approximate inverse for non-symmetric linear systems
The concept of supernodes, originally developed to accelerate direct solution methods for linear systems, is generalized to block factorized sparse...
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The parameterized upper and lower triangular splitting methods for saddle point problems
In this paper, we propose a class of parameterized upper and lower triangular splitting (denoted by PULTS) methods for solving nonsingular saddle...
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Updating preconditioners for modified least squares problems
In this paper, we analyze how to update incomplete Cholesky preconditioners to solve least squares problems using iterative methods when the set of...
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Multistep matrix splitting iteration preconditioning for singular linear systems
Multistep matrix splitting iterations serve as preconditioning for Krylov subspace methods for solving singular linear systems. The preconditioner is...
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A Legendre spectral quadrature Galerkin method for the Cauchy-Navier equations of elasticity with variable coefficients
We solve the Dirichlet and mixed Dirichlet-Neumann boundary value problems for the variable coefficient Cauchy-Navier equations of elasticity in a...
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An inexact modified relaxed splitting preconditioner for the generalized saddle point problems from the incompressible Navier-Stokes equations
Based on the modified relaxed splitting (MRS) preconditioner proposed by Fan and Zhu (Appl. Math. Lett. 55 , 18–26
2016 ), an inexact modified relaxed... -
A modified generalized shift-splitting preconditioner for nonsymmetric saddle point problems
For the nonsymmetric saddle point problems with nonsymmetric positive definite (1,1) parts, the modified generalized shift-splitting (MGSS)...
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A new relaxed HSS preconditioner for saddle point problems
We present a preconditioner for saddle point problems. The proposed preconditioner is extracted from a stationary iterative method which is...
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Solving mixed classical and fractional partial differential equations using short–memory principle and approximate inverses
The efficient numerical solution of the large linear systems of fractional differential equations is considered here. The key tool used is the short–me...
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A generalized modified HSS method for singular complex symmetric linear systems
In this paper, based on the Hermitian and skew-Hermitian splitting, we give a generalized modified Hermitian and skew-Hermitian splitting (GMHSS)...
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Modified parameterized inexact Uzawa method for singular saddle-point problems
As well known, each of the consistent singular saddle-point (CSSP) problems has more than one solutions, and most of the iteration methods can only...
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On generalized parameterized inexact Uzawa methods for singular saddle-point problems
For a class of nonsingular saddle-point problems, Bai et al. in 2008 studied an efficient parameterized inexact Uzawa (PIU) method; see [Z.-Z. Bai,...
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Limited-memory LDL⊤ factorization of symmetric quasi-definite matrices with application to constrained optimization
We propose a generalization of the limited-memory Cholesky factorization of Lin and Moré (SIAM J. Sci. Comput. 21 (1), 24–45,
1999 ) to the symmetric... -
A note on semi-convergence of generalized parameterized inexact Uzawa method for singular saddle point problems
Recently, Zhang and Wang studied the generalized parameterized inexact Uzawa (GPIU) method for singular saddle point problems, see Zhang and Wang...
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The effect of graph partitioning techniques on parallel Block FSAI preconditioning: a computational study
Adaptive Block FSAI (ABF) is a novel preconditioner which has proved efficient for the parallel solution of symmetric positive definite (SPD) linear...