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Journal articles on the topic 'Preconditioned Krylov subspace method'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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1

Gryazin, Yury. "Preconditioned Krylov Subspace Methods for Sixth Order Compact Approximations of the Helmholtz Equation." ISRN Computational Mathematics 2014 (January 21, 2014): 1–15. http://dx.doi.org/10.1155/2014/745849.

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We consider an efficient iterative approach to the solution of the discrete Helmholtz equation with Dirichlet, Neumann, and Sommerfeld-like boundary conditions based on a compact sixth order approximation scheme and lower order preconditioned Krylov subspace methodology. The resulting systems of finite-difference equations are solved by different preconditioned Krylov subspace-based methods. In the analysis of the lower order preconditioning developed here, we introduce the term “kth order preconditioned matrix” in addition to the commonly used “an optimal preconditioner.” The necessity of the

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2

Liu, Jia. "An Alternative HSS Preconditioner for the Unsteady Incompressible Navier-Stokes Equations in Rotation Form." Journal of Applied Mathematics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/307939.

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We study the preconditioned iterative method for the unsteady Navier-Stokes equations. The rotation form of the Oseen system is considered. We apply an efficient preconditioner which is derived from the Hermitian/Skew-Hermitian preconditioner to the Krylov subspace-iterative method. Numerical experiments show the robustness of the preconditioned iterative methods with respect to the mesh size, Reynolds numbers, time step, and algorithm parameters. The preconditioner is efficient and easy to apply for the unsteady Oseen problems in rotation form.

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3

Chen, Dandan, Ting-Zhu Huang, and Liang Li. "Comparison of Algebraic Multigrid Preconditioners for Solving Helmholtz Equations." Journal of Applied Mathematics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/367909.

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An algebraic multigrid (AMG) with aggregation technique to coarsen is applied to construct a better preconditioner for solving Helmholtz equations in this paper. The solution process consists of constructing the preconditioner by AMG and solving the preconditioned Helmholtz problems by Krylov subspace methods. In the setup process of AMG, we employ the double pairwise aggregation (DPA) scheme firstly proposed by Y. Notay (2006) as the coarsening method. We compare it with the smoothed aggregation algebraic multigrid and meanwhile show shifted Laplacian preconditioners. According to numerical r

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4

Huang, Yunying, and Guoliang Chen. "A relaxed block splitting preconditioner for complex symmetric indefinite linear systems." Open Mathematics 16, no. 1 (2018): 561–73. http://dx.doi.org/10.1515/math-2018-0051.

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AbstractIn this paper, we propose a relaxed block splitting preconditioner for a class of complex symmetric indefinite linear systems to accelerate the convergence rate of the Krylov subspace iteration method and the relaxed preconditioner is much closer to the original block two-by-two coefficient matrix. We study the spectral properties and the eigenvector distributions of the corresponding preconditioned matrix. In addition, the degree of the minimal polynomial of the preconditioned matrix is also derived. Finally, some numerical experiments are presented to illustrate the effectiveness of

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5

Zheng, Zhong, and Guo Feng Zhang. "A Block Diagonal Preconditioner for Generalised Saddle Point Problems." East Asian Journal on Applied Mathematics 6, no. 3 (2016): 235–52. http://dx.doi.org/10.4208/eajam.260815.280216a.

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AbstractA lopsided alternating direction iteration (LADI) method and an induced block diagonal preconditioner for solving block two-by-two generalised saddle point problems are presented. The convergence of the LADI method is analysed, and the block diagonal preconditioner can accelerate the convergence rates of Krylov subspace iteration methods such as GMRES. Our new preconditioned method only requires a solver for two linear equation sub-systems with symmetric and positive definite coefficient matrices. Numerical experiments show that the GMRES with the new preconditioner is quite effective.

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6

Oliveira, Suely, and Yuanhua Deng. "Preconditioned Krylov subspace methods for transport equations." Progress in Nuclear Energy 33, no. 1-2 (1998): 155–74. http://dx.doi.org/10.1016/s0149-1970(97)00099-1.

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7

Chan, T. F., E. Chow, Y. Saad, and M. C. Yeung. "Preserving Symmetry in Preconditioned Krylov Subspace Methods." SIAM Journal on Scientific Computing 20, no. 2 (1998): 568–81. http://dx.doi.org/10.1137/s1064827596311554.

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8

Li, Cheng-Liang, and Chang-Feng Ma. "On Euler preconditioned SHSS iterative method for a class of complex symmetric linear systems." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 5 (2019): 1607–27. http://dx.doi.org/10.1051/m2an/2019029.

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In this paper, we propose an Euler preconditioned single-step HSS (EP-SHSS) iterative method for solving a broad class of complex symmetric linear systems. The proposed method can be applied not only to the non-singular complex symmetric linear systems but also to the singular ones. The convergence (semi-convergence) properties of the proposed method are carefully discussed under suitable restrictions. Furthermore, we consider the acceleration of the EP-SHSS method by preconditioned Krylov subspace method and discuss the spectral properties of the corresponding preconditioned matrix. Numerical

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9

Hu, Zixiang, Shi Zhang, Yun Zhang, Huamin Zhou, and Dequn Li. "An efficient preconditioned Krylov subspace method for large-scale finite element equations with MPC using Lagrange multiplier method." Engineering Computations 31, no. 7 (2014): 1169–97. http://dx.doi.org/10.1108/ec-03-2013-0077.

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Purpose – The purpose of this paper is to propose an efficient iterative method for large-scale finite element equations of bad numerical stability arising from deformation analysis with multi-point constraint using Lagrange multiplier method. Design/methodology/approach – In this paper, taking warpage analysis of polymer injection molding based on surface model as an example, the performance of several popular Krylov subspace methods, including conjugate gradient, BiCGSTAB and generalized minimal residual (GMRES), with diffident Incomplete LU (ILU)-type preconditions is investigated and compa

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10

Vuik, C. "Krylov Subspace Solvers and Preconditioners." ESAIM: Proceedings and Surveys 63 (2018): 1–43. http://dx.doi.org/10.1051/proc/201863001.

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In these lecture notes an introduction to Krylov subspace solvers and preconditioners is presented. After a discretization of partial differential equations large, sparse systems of linear equations have to be solved. Fast solution of these systems is very urgent nowadays. The size of the problems can be 1013 unknowns and 1013 equations. Iterative solution methods are the methods of choice for these large linear systems. We start with a short introduction of Basic Iterative Methods. Thereafter preconditioned Krylov subspace methods, which are state of the art, are describeed. A distinction is

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11

Hochbruck, Marlis, and Gerhard Starke. "Preconditioned Krylov Subspace Methods for Lyapunov Matrix Equations." SIAM Journal on Matrix Analysis and Applications 16, no. 1 (1995): 156–71. http://dx.doi.org/10.1137/s0895479892239238.

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12

Li, Yan-Ran, Xin-Hui Shao, and Shi-Yu Li. "New Preconditioned Iteration Method Solving the Special Linear System from the PDE-Constrained Optimal Control Problem." Mathematics 9, no. 5 (2021): 510. http://dx.doi.org/10.3390/math9050510.

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In many fields of science and engineering, partial differential equation (PDE) constrained optimal control problems are widely used. We mainly solve the optimization problem constrained by the time-periodic eddy current equation in this paper. We propose the three-block splitting (TBS) iterative method and proved that it is unconditionally convergent. At the same time, the corresponding TBS preconditioner is derived from the TBS iteration method, and we studied the spectral properties of the preconditioned matrix. Finally, numerical examples in two-dimensions is applied to demonstrate the adva

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13

Li, Cui-Xia, Yan-Jun Liang, and Shi-Liang Wu. "Generalized Preconditioned MHSS Method for a Class of Complex Symmetric Linear Systems." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/206821.

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Based on the modified Hermitian and skew-Hermitian splitting (MHSS) and preconditioned MHSS (PMHSS) methods, a generalized preconditioned MHSS (GPMHSS) method for a class of complex symmetric linear systems is presented. Theoretical analysis gives an upper bound for the spectral radius of the iteration matrix. From a practical point of view, we have analyzed and implemented inexact GPMHSS (IGPMHSS) iteration, which employs Krylov subspace methods as its inner processes. Numerical experiments are reported to confirm the efficiency of the proposed methods.

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14

Bai, Zhong-Zhi. "Regularized HSS iteration methods for stabilized saddle-point problems." IMA Journal of Numerical Analysis 39, no. 4 (2018): 1888–923. http://dx.doi.org/10.1093/imanum/dry046.

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Abstract We extend the regularized Hermitian and skew-Hermitian splitting (RHSS) iteration methods for standard saddle-point problems to stabilized saddle-point problems and establish the corresponding unconditional convergence theory for the resulting methods. Besides being used as stationary iterative solvers, this class of RHSS methods can also be used as preconditioners for Krylov subspace methods. It is shown that the eigenvalues of the corresponding preconditioned matrix are clustered at a small number of points in the interval $(0, \, 2)$ when the iteration parameter is close to $0$ and

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15

Chow, Edmond, and Yousef Saad. "Preconditioned Krylov Subspace Methods for Sampling Multivariate Gaussian Distributions." SIAM Journal on Scientific Computing 36, no. 2 (2014): A588—A608. http://dx.doi.org/10.1137/130920587.

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16

Yu, Chun Xiao. "A Kind of Preconditioned IGMRES(m) Algorithm." Advanced Materials Research 482-484 (February 2012): 413–16. http://dx.doi.org/10.4028/www.scientific.net/amr.482-484.413.

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Fundamental theories are studied for an Incomplete Generalized Minimal Residual Method(IGMRES(m)) in Krylov subspace. An algebraic equations generated from the IGMRES(m) algorithm is presented. The relationships are deeply researched for the algorithm convergence and the coefficient matrix of the equations. A kind of preconditioned method is proposed to improve the convergence of the IGMRES(m) algorithm. It is proved that the best convergence can be obtained through appropriate matrix decomposition.

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17

Liang, Qiao, and Qiang Ye. "Deflation by restriction for the inverse-free preconditioned Krylov subspace method." Numerical Algebra, Control and Optimization 6, no. 1 (2016): 55–71. http://dx.doi.org/10.3934/naco.2016.6.55.

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18

Yin, jun-Feng, Ken Hayami, and Zhong-Zhi Bai. "Preconditioned Krylov subspace method for the solution of least-squares problems." PAMM 7, no. 1 (2007): 2020151–52. http://dx.doi.org/10.1002/pamm.200701146.

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19

Liu, Qingbing. "New Preconditioners for Nonsymmetric Saddle Point Systems with Singular (1,1) Block." ISRN Computational Mathematics 2013 (August 27, 2013): 1–8. http://dx.doi.org/10.1155/2013/507817.

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We investigate the solution of large linear systems of saddle point type with singular (1,1) block by preconditioned iterative methods and consider two parameterized block triangular preconditioners used with Krylov subspace methods which have the attractive property of improved eigenvalue clustering with increased ill-conditioning of the (1,1) block of the saddle point matrix, including the choice of the parameter. Meanwhile, we analyze the spectral characteristics of two preconditioners and give the optimal parameter in practice. Numerical experiments that validate the analysis are presented

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20

Türk, U., and A. Ecder. "NUMERICAL INVESTIGATION OF THE POLYMER MELT FLOW IN INJECTION MOLDING BY USING ILU PRECONDITIONED GMRES." Mathematical Modelling and Analysis 4, no. 1 (1999): 174–84. http://dx.doi.org/10.3846/13926292.1999.9637122.

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The implementation of a modern preconditioned Newton‐Krylov solvers to the polymer melt flow in injection molding is the main focus of this paper. The viscoelastic and non‐isothermal characteristics of the transient polymer flow is simulated numerically and the highly non‐linear problem solved. This non‐linear behavior results from the combination of the dominant convective terms and the dependence of the polymer viscosity to the changing temperature and the shear rate. The governing non‐Newtonian fluid flow and energy equations with appropriate approximations are discretized by finite differe

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21

Ikuno, Soichiro, Gong Chen, Taku Itoh, Susumu Nakata, and Kuniyoshi Abe. "Variable Preconditioned Krylov Subspace Method With Communication Avoiding Technique for Electromagnetic Analysis." IEEE Transactions on Magnetics 53, no. 6 (2017): 1–4. http://dx.doi.org/10.1109/tmag.2017.2655513.

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22

Golub, Gene H., and Qiang Ye. "An Inverse Free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems." SIAM Journal on Scientific Computing 24, no. 1 (2002): 312–34. http://dx.doi.org/10.1137/s1064827500382579.

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23

Chernesky, Michael P. "On preconditioned Krylov subspace methods for discrete convection-diffusion problems." Numerical Methods for Partial Differential Equations 13, no. 4 (1997): 321–30. http://dx.doi.org/10.1002/(sici)1098-2426(199707)13:4<321::aid-num2>3.0.co;2-n.

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24

Li, Cui-Xia, and Shi-Liang Wu. "A Double-Parameter GPMHSS Method for a Class of Complex Symmetric Linear Systems from Helmholtz Equation." Mathematical Problems in Engineering 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/894242.

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Based on the preconditioned MHSS (PMHSS) and generalized PMHSS (GPMHSS) methods, a double-parameter GPMHSS (DGPMHSS) method for solving a class of complex symmetric linear systems from Helmholtz equation is presented. A parameter region of the convergence for DGPMHSS method is provided. From practical point of view, we have analyzed and implemented inexact DGPMHSS (IDGPMHSS) iteration, which employs Krylov subspace methods as its inner processes. Numerical examples are reported to confirm the efficiency of the proposed methods.

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25

Kumagai, Makoto, Shimpei Kakita, and Yoshifumi Okamoto. "Performance of Krylov subspace method with SOR preconditioner supported by Eisenstat’s technique for linear system derived from time-periodic FEM." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 38, no. 5 (2019): 1641–54. http://dx.doi.org/10.1108/compel-12-2018-0492.

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Purpose This paper aims to present the affinity of BiCGStab and BiCGStab2 with successive over-relaxation (SOR) preconditioner supported by Eisenstat’s technique for a linear system derived from the time-periodic finite element method (TP-FEM). To solve the time domain electromagnetic field problem with long transient state, TP-FEM is very useful from the perspective of rapidly achieving a steady state. Because TP-FEM solves all of the state variables at once, the linear system derived from TP-FEM becomes the large scale and nonsymmetric, whereas the detailed performance of some preconditioned

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26

Chen, Zhongying, Dongsheng Cheng, Wei Feng, Tingting Wu, and Hongqi Yang. "A multigrid-based preconditioned Krylov subspace method for the Helmholtz equation with PML." Journal of Mathematical Analysis and Applications 383, no. 2 (2011): 522–40. http://dx.doi.org/10.1016/j.jmaa.2011.05.054.

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27

Quillen, Patrick, and Qiang Ye. "A block inverse-free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems." Journal of Computational and Applied Mathematics 233, no. 5 (2010): 1298–313. http://dx.doi.org/10.1016/j.cam.2008.10.071.

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28

Zhang, Jun. "Preconditioned Krylov subspace methods for solving nonsymmetric matrices from CFD applications." Computer Methods in Applied Mechanics and Engineering 189, no. 3 (2000): 825–40. http://dx.doi.org/10.1016/s0045-7825(99)00345-x.

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29

Wang, Shun, Eric de Sturler, and Glaucio H. Paulino. "Large-scale topology optimization using preconditioned Krylov subspace methods with recycling." International Journal for Numerical Methods in Engineering 69, no. 12 (2007): 2441–68. http://dx.doi.org/10.1002/nme.1798.

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30

Moutafis, Byron E., George A. Gravvanis, and Christos K. Filelis-Papadopoulos. "Hybrid multi-projection method using sparse approximate inverses on GPU clusters." International Journal of High Performance Computing Applications 34, no. 3 (2020): 282–305. http://dx.doi.org/10.1177/1094342020905637.

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The state-of-the-art supercomputing infrastructures are equipped with accelerators, such as graphics processing units (GPUs), that operate as coprocessors for each workstation of the distributed memory system. The multi-projection type methods are a class of algebraic domain decomposition methods based on semi-aggregation techniques. The multi-projection type methods have improved convergence behavior, as the number of subdomains increases, due to the corresponding augmentation of the semi-aggregated local linear systems with more coarse components, while the number of fine components is reduc

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31

Gazzola, Silvia, and Paolo Novati. "Some transpose-free CG-like solvers for nonsymmetric ill-posed problems." Journal of Numerical Mathematics 28, no. 1 (2020): 15–32. http://dx.doi.org/10.1515/jnma-2018-0107.

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AbstractThis paper introduces and analyzes an original class of Krylov subspace methods that provide an efficient alternative to many well-known conjugate-gradient-like (CG-like) Krylov solvers for square nonsymmetric linear systems arising from discretizations of inverse ill-posed problems. The main idea underlying the new methods is to consider some rank-deficient approximations of the transpose of the system matrix, obtained by running the (transpose-free) Arnoldi algorithm, and then apply some Krylov solvers to a formally right-preconditioned system of equations. Theoretical insight is giv

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32

Zhang, Ke, and Chuanqing Gu. "A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand Sides." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/457089.

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The restarted global CMRH method (Gl-CMRH(m)) (Heyouni, 2001) is an attractive method for linear systems with multiple right-hand sides. However, Gl-CMRH(m) may converge slowly or even stagnate due to a limited Krylov subspace. To ameliorate this drawback, a polynomial preconditioned variant of Gl-CMRH(m) is presented. We give a theoretical result for the square case that assures that the number of restarts can be reduced with increasing values of the polynomial degree. Numerical experiments from real applications are used to validate the effectiveness of the proposed method.

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33

Damm, T. "Direct methods and ADI-preconditioned Krylov subspace methods for generalized Lyapunov equations." Numerical Linear Algebra with Applications 15, no. 9 (2008): 853–71. http://dx.doi.org/10.1002/nla.603.

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34

Axelsson, Owe, Maya Neytcheva, and Zhao-Zheng Liang. "PARALLEL SOLUTION METHODS AND PRECONDITIONERS FOR EVOLUTION EQUATIONS." Mathematical Modelling and Analysis 23, no. 2 (2018): 287–308. http://dx.doi.org/10.3846/mma.2018.018.

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The recent development of the high performance computer platforms shows a clear trend towards heterogeneity and hierarchy. In order to utilize the computational power, particular attention must be paid to ﬁnding new algorithms or adjust existing ones so that they better match the HPC computer architecture. In this work we consider an alternative to classical time-stepping methods based on use of time-harmonic properties and discuss solution approaches that allow eﬃcient utilization of modern HPC resources. The method in focus is based on a truncated Fourier expansion of the solution of an evol

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35

Luo, Wei-Hua, and Ting-Zhu Huang. "A Parameterized Splitting Preconditioner for Generalized Saddle Point Problems." Journal of Applied Mathematics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/489295.

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By using Sherman-Morrison-Woodbury formula, we introduce a preconditioner based on parameterized splitting idea for generalized saddle point problems which may be singular and nonsymmetric. By analyzing the eigenvalues of the preconditioned matrix, we find that whenαis big enough, it has an eigenvalue at 1 with multiplicity at leastn, and the remaining eigenvalues are all located in a unit circle centered at 1. Particularly, when the preconditioner is used in general saddle point problems, it guarantees eigenvalue at 1 with the same multiplicity, and the remaining eigenvalues will tend to 1 as

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36

Amini, S., and N. D. Maines. "Preconditioned Krylov subspace methods for boundary element solution of the Helmholtz equation." International Journal for Numerical Methods in Engineering 41, no. 5 (1998): 875–98. http://dx.doi.org/10.1002/(sici)1097-0207(19980315)41:5<875::aid-nme313>3.0.co;2-9.

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37

Axelsson, Owe, Shiraz Farouq, and Maya Neytcheva. "Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems." Numerical Algorithms 73, no. 3 (2016): 631–63. http://dx.doi.org/10.1007/s11075-016-0111-1.

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38

Axelsson, Owe, Shiraz Farouq, and Maya Neytcheva. "Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems." Numerical Algorithms 74, no. 1 (2016): 19–37. http://dx.doi.org/10.1007/s11075-016-0136-5.

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39

Ran, Yu-Hong, Jun-Gang Wang, and Dong-Ling Wang. "On Preconditioners Based on HSS for the Space Fractional CNLS Equations." East Asian Journal on Applied Mathematics 7, no. 1 (2017): 70–81. http://dx.doi.org/10.4208/eajam.190716.051116b.

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AbstractThe space fractional coupled nonlinear Schrödinger (CNLS) equations are discretized by an implicit conservative difference scheme with the fractional centered difference formula, which is unconditionally stable. The coefficient matrix of the discretized linear system is equal to the sum of a complex scaled identity matrix which can be written as the imaginary unit times the identity matrix and a symmetric Toeplitz-plusdiagonal matrix. In this paper, we present new preconditioners based on Hermitian and skew-Hermitian splitting (HSS) for such Toeplitz-like matrix. Theoretically, we show

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40

Vuik, Kees, Agur G. J. Sevink, and Gérard C. Herman. "A Preconditioned Krylov Subspace Method for the Solution of Least Squares Problems in Inverse Scattering." Journal of Computational Physics 123, no. 2 (1996): 330–40. http://dx.doi.org/10.1006/jcph.1996.0027.

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Ahmad, Shahbaz, Adel M. Al-Mahdi, and Rashad Ahmed. "Two new preconditioners for mean curvature-based image deblurring problem." AIMS Mathematics 6, no. 12 (2021): 13824–44. http://dx.doi.org/10.3934/math.2021802.

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<abstract><p>The mean curvature-based image deblurring model is widely used to enhance the quality of the deblurred images. However, the discretization of the associated Euler-Lagrange equations produce a nonlinear ill-conditioned system which affect the convergence of the numerical algorithms like Krylov subspace methods. To overcome this difficulty, in this paper, we present two new symmetric positive definite (SPD) preconditioners. An efficient algorithm is presented for the mean curvature-based image deblurring problem which combines a fixed point iteration (FPI) with new preco

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42

Nordsveen, Magnus, and Randi Moe. "Preconditioned Krylov subspace methods used in solving two-dimensional transient two-phase flows." International Journal for Numerical Methods in Fluids 31, no. 7 (1999): 1141–56. http://dx.doi.org/10.1002/(sici)1097-0363(19991215)31:7<1141::aid-fld916>3.0.co;2-g.

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Ghai, Aditi, Cao Lu, and Xiangmin Jiao. "A comparison of preconditioned Krylov subspace methods for large‐scale nonsymmetric linear systems." Numerical Linear Algebra with Applications 26, no. 1 (2018): e2215. http://dx.doi.org/10.1002/nla.2215.

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44

Badri, M. A., P. Jolivet, B. Rousseau, and Y. Favennec. "Preconditioned Krylov subspace methods for solving radiative transfer problems with scattering and reflection." Computers & Mathematics with Applications 77, no. 6 (2019): 1453–65. http://dx.doi.org/10.1016/j.camwa.2018.09.041.

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Wu, Shu-Lin, and Tao Zhou. "Diagonalization-based parallel-in-time algorithms for parabolic PDE-constrained optimization problems." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 88. http://dx.doi.org/10.1051/cocv/2020012.

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Solving parabolic PDE-constrained optimization problems requires to take into account the discrete time points all-at-once, which means that the computation procedure is often time-consuming. It is thus desirable to design robust and analyzable parallel-in-time (PinT) algorithms to handle this kind of coupled PDE systems with opposite evolution directions. To this end, for two representative model problems which are, respectively, the time-periodic PDEs and the initial-value PDEs, we propose a diagonalization-based approach that can reduce dramatically the computational time. The main idea lie

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46

Badahmane, A., A. H. Bentbib, and H. Sadok. "Preconditioned Krylov subspace and GMRHSS iteration methods for solving the nonsymmetric saddle point problems." Numerical Algorithms 84, no. 4 (2019): 1295–312. http://dx.doi.org/10.1007/s11075-019-00833-4.

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47

GONZALEZ, PATRICIA, JOSE C. CABALEIRO, and TOMAS F. PENA. "PARALLEL INCOMPLETE LU FACTORIZATION AS A PRECONDITIONER FOR KRYLOV SUBSPACE METHODS." Parallel Processing Letters 09, no. 04 (1999): 467–74. http://dx.doi.org/10.1142/s0129626499000438.

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In this paper we describe a new method for the ILU(0) factorization of sparse systems in distributed memory multiprocessor architectures. This method uses a symbolic reordering technique, so the final system can be grouped in blocks where the rows are independent and the factorization of these entries can be carried out in parallel. The parallel ILU(0) factorization has been tested on the Cray T3E multicomputer using the MPI communication library. The performance was analysed using matrices from the Harwell–Boeing collection.

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48

Badahmane, A., A. H. Bentbib, and H. Sadok. "Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides." ETNA - Electronic Transactions on Numerical Analysis 51 (2019): 495–511. http://dx.doi.org/10.1553/etna_vol51s495.

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49

Wang, Qinghua, and Yogendra Joshi. "Algebraic Multigrid Preconditioned Krylov Subspace Methods for Fluid Flow and Heat Transfer on Unstructured Meshes." Numerical Heat Transfer, Part B: Fundamentals 49, no. 3 (2006): 197–221. http://dx.doi.org/10.1080/10407790500290725.

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Yun, Jae H. "Performance of relaxed iterative methods for image deblurring problems." Journal of Algorithms & Computational Technology 13 (January 2019): 174830261986173. http://dx.doi.org/10.1177/1748302619861732.

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Abstract:

In this paper, we consider performance of relaxation iterative methods for four types of image deblurring problems with different regularization terms. We first study how to apply relaxation iterative methods efficiently to the Tikhonov regularization problems, and then we propose how to find good preconditioners and near optimal relaxation parameters which are essential factors for fast convergence rate and computational efficiency of relaxation iterative methods. We next study efficient applications of relaxation iterative methods to Split Bregman method and the fixed point method for solvin

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