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ON A SPLITTING PRECONDITIONER FOR SADDLE POINT PROBLEMS
SALKUYEH, DAVOD KHOJASTEH,ABDOLMALEKI, MARYAM,KARIMI, SAEED The Korean Society for Computational and Applied M 2018 Journal of applied mathematics & informatics Vol.36 No.5
Cao et al. in (Numer. Linear. Algebra Appl. 18 (2011) 875-895) proposed a splitting method for saddle point problems which unconditionally converges to the solution of the system. It was shown that a Krylov subspace method like GMRES in conjunction with the induced preconditioner is very effective for the saddle point problems. In this paper we first modify the iterative method, discuss its convergence properties and apply the induced preconditioner to the problem. Numerical experiments of the corresponding preconditioner are compared to the primitive one to show the superiority of our method.
A PRECONDITIONER FOR THE NORMAL EQUATIONS
Salkuyeh, Davod Khojasteh The Korean Society for Computational and Applied M 2010 Journal of applied mathematics & informatics Vol.28 No.3
In this paper, an algorithm for computing the sparse approximate inverse factor of matrix $A^{T}\;A$, where A is an $m\;{\times}\;n$ matrix with $m\;{\geq}\;n$ and rank(A) = n, is proposed. The computation of the inverse factor are done without computing the matrix $A^{T}\;A$. The computed sparse approximate inverse factor is applied as a preconditioner for solving normal equations in conjunction with the CGNR algorithm. Some numerical experiments on test matrices are presented to show the efficiency of the method. A comparison with some available methods is also included.
A SPARSE APPROXIMATE INVERSE PRECONDITIONER FOR NONSYMMETRIC POSITIVE DEFINITE MATRICES
Salkuyeh, Davod Khojasteh The Korean Society for Computational and Applied M 2010 Journal of applied mathematics & informatics Vol.28 No.5
We develop an algorithm for computing a sparse approximate inverse for a nonsymmetric positive definite matrix based upon the FFAPINV algorithm. The sparse approximate inverse is computed in the factored form and used to work with some Krylov subspace methods. The preconditioner is breakdown free and, when used in conjunction with Krylov-subspace-based iterative solvers such as the GMRES algorithm, results in reliable solvers. Some numerical experiments are given to show the efficiency of the preconditioner.
SPECTRAL ANALYSIS OF THE MGSS PRECONDITIONER FOR SINGULAR SADDLE POINT PROBLEMS
Maryam Rahimian,Davod Khojasteh Salkuyeh 한국전산응용수학회 2020 Journal of applied mathematics & informatics Vol.38 No.1
Recently Salkuyeh and Rahimian in (Comput. Math. Appl. 74 (2017) 2940-2949) proposed a modification of the generalized shift-splitting (MGSS) method for solving singular saddle point problems. In this paper, we present the spectral analysis of the MGSS preconditioner when it is applied to precondition the singular saddle point problems with the (1,1) block being symmetric. Some eigenvalue bounds for the spectrum of the preconditioned matrix are given. We show that all the real eigenvalues of the preconditioned matrix are in a positive interval and all nonzero eigenvalues having nonzero imaginary part are contained in an intersection of two circles.
SPECTRAL ANALYSIS OF THE MGSS PRECONDITIONER FOR SINGULAR SADDLE POINT PROBLEMS
RAHIMIAN, MARYAM,SALKUYEH, DAVOD KHOJASTEH The Korean Society for Computational and Applied M 2020 Journal of applied mathematics & informatics Vol.38 No.1
Recently Salkuyeh and Rahimian in (Comput. Math. Appl. 74 (2017) 2940-2949) proposed a modification of the generalized shift-splitting (MGSS) method for solving singular saddle point problems. In this paper, we present the spectral analysis of the MGSS preconditioner when it is applied to precondition the singular saddle point problems with the (1, 1) block being symmetric. Some eigenvalue bounds for the spectrum of the preconditioned matrix are given. We show that all the real eigenvalues of the preconditioned matrix are in a positive interval and all nonzero eigenvalues having nonzero imaginary part are contained in an intersection of two circles.
Optimal Video Packet Distribution in Multipath Routing for Urban VANETs
Mostafa Asgharpoor Salkuyeh,Bahman Abolhassani 한국통신학회 2018 Journal of communications and networks Vol.20 No.2
Video content streaming between two vehicles hasvarious applications in vehicular ad-hoc networks (VANETs). Dueto the highly dynamic nature of VANETs, video contents areusually transferred via multiple discovered routes to increase thechance of error-free packet delivery. However, vehicular routessuffer from limited lifetimes and low connectivity probabilities,which result in increasing packet loss ratio (PLR) and frequentvideo playback freezing. In this paper, PLR is minimized byoptimally distributing video packets in multiple routes whilemeeting quality of service (QoS) parameters (meeting freezingdelay and number of transferred video packets constraints). Bydoing so, reconstruction and playback of the video are achievedwith guaranteed QoS. Performance evaluation of our proposedscheme shows enhancements in terms of average PLR (63.3%),average freezing delay (6%), average packet end-to-end delay(66.6%) and average number of delivered video packets (8%) after10 seconds simulation.
A PRECONDITIONER FOR THE NORMAL EQUATIONS
Davod Khojasteh Salkuyeh 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.3
In this paper, an algorithm for computing the sparse approximate inverse factor of matrix ATA, where A is an m × n matrix with m ≥ n and rank(A) = n, is proposed. The computation of the inverse factor are done without computing the matrix ATA. The computed sparse approximate inverse factor is applied as a preconditioner for solving normal equations in conjunction with the CGNR algorithm. Some numerical experiments on test matrices are presented to show the efficiency of the method. A comparison with some available methods is also included.
ON A SPLITTING PRECONDITIONER FOR SADDLE POINT PROBLEMS
Davod Khojasteh Salkuyeh,MARYAM ABDOLMALEKI,SAEED KARIMI 한국전산응용수학회 2018 Journal of applied mathematics & informatics Vol.36 No.5
Cao et al. in (Numer. Linear. Algebra Appl. 18 (2011) 875-895) proposed a splitting method for saddle point problems which un- conditionally converges to the solution of the system. It was shown that a Krylov subspace method like GMRES in conjunction with the induced preconditioner is very eective for the saddle point problems. In this paper we rst modify the iterative method, discuss its convergence properties and apply the induced preconditioner to the problem. Numerical experiments of the corresponding preconditioner are compared to the primitive one to show the superiority of our method.
BILUS: a block version of ILUS factorization
Davod K. Salkuyeh,Faezeh Toutounian 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.15 No.-
ILUS factorization has many desirable properties such as itsamenability to the skyline format, the ease with which stability may bemonitored, and the possibility of constructing a preconditioner with sym-metric structure. In this paper we introduce a new preconditioning tech-nique for general sparse linear systems based on the ILUS factorizationstrategy. The resulting preconditioner has the same properties as the ILUSpreconditioner. Some theoretical properties of the new preconditioner arediscussed and numerical experiments on test matrices from the Harwell-Boeing collection are tested. Our results indicate that the new precondi-tioner is cheaper to construct than the ILUS preconditioner.
A SPARSE APPROXIMATE INVERSE PRECONDITIONER FOR NONSYMMETRIC POSITIVE DEFINITE MATRICES
Davod Khojasteh Salkuyeh 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.5
We develop an algorithm for computing a sparse approximate inverse for a nonsymmetric positive definite matrix based upon the FFAPINV algorithm. The sparse approximate inverse is computed in the factored form and used to work with some Krylov subspace methods. The preconditioner is breakdown free and, when used in conjunction with Krylov-subspace-based iterative solvers such as the GMRES algorithm, results in reliable solvers. Some numerical experiments are given to show the efficiency of the preconditioner.