Accelerated double-step scale splitting iteration method for solving a class of complex symmetric linear systems

Dehghan, Mehdi; Shirilord, Akbar

doi:10.1007/s11075-019-00682-1

Cited by 18 publications

(4 citation statements)

References 20 publications

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“…Moreover, some derivative-free iterative methods were developed for solving nonlinear equations [38,39]. Furthermore, some alternative approaches were conducted for solving complex symmetric linear systems [40] or a Sylvester matrix equation [41].…”

Section: Overview Of Methods For Solving Snementioning

confidence: 99%

Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations

et al. 2023

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This research proposes and investigates some improvements in gradient descent iterations that can be applied for solving system of nonlinear equations (SNE). In the available literature, such methods are termed improved gradient descent methods. We use verified advantages of various accelerated double direction and double step size gradient methods in solving single scalar equations. Our strategy is to control the speed of the convergence of gradient methods through the step size value defined using more parameters. As a result, efficient minimization schemes for solving SNE are introduced. Linear global convergence of the proposed iterative method is confirmed by theoretical analysis under standard assumptions. Numerical experiments confirm the significant computational efficiency of proposed methods compared to traditional gradient descent methods for solving SNE.

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Section: Overview Of Methods For Solving Snementioning

confidence: 99%

Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations

et al. 2023

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“…Several iteration methods have been introduced for solving the linear system (1.1) as; Hermitian and skew-Hermitian splitting (HSS) iteration method [8], accelerated HSS (AHSS) [10], modified HSS (MHSS) [7], preconditioned MHSS (PMHSS) [9], generalized PMHSS (GPMHSS) [18], skew-normal splitting (SNS) [6], modified skew-normal splitting (MSNS) [28], lopsided PMHSS (LPMHSS) [26], combination of real and imaginary parts (CRI) [32], twostep scale-splitting (TSCSP) [29], two-parameter TSCSP (TTSCSP) [30], double-step scale splitting (DSS) [33] and accelerated DSS (ADSS) [17] method. Now here we will briefly describe the PMHSS, LPMHSS, TSCSP and TTSCSP iteration methods for solving linear system (1.1).…”

Section: Introductionmentioning

confidence: 99%

“…Their main goal was to increase the convergence speed of TSCSP method. In the following we describe the TTSCSP iteration method (See also ADSS method [17]). TTSCSP iteration method [30]: For a given initial guess 0 ∈ ℂ n , compute the iterate j+1 according to: where 1 and 2 are real positive constants.…”

Section: Introductionmentioning

confidence: 99%

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Two lopsided TSCSP (LTSCSP) iteration methods for solution of complex symmetric positive definite linear systems

Dehghan

Shirilord

2020

Engineering with Computers

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In this paper we make two new lopsided methods (LTSCSP1 and LTSCSP2) based on the two-scale-splitting (TSCSP) method and show that the convergence speed of TSCSP iteration method can be increased under some conditions without adding any additional parameter. The convergence analysis of the new methods in detail is given. Then we will obtain the quasi-optimal parameter to minimize the spectral radius of iteration matrix for the new methods. The inexact version of these methods is derived. To illustrate the effectiveness of the proposed framework, several numerical examples are given.

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Improved Linear and Nonlinear Iterative Methods for Rainfall Infiltration Simulation

Zhou

2023

SpringerBriefs in Applied Sciences and Technology

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The linear infiltration equations obtained by discretizing Richards’ equation need to be solved iteratively, including two approaches of linear and nonlinear iterations. The first method is to use numerical methods to directly numerically discretize Richards’ equations to obtain nonlinear ordinary differential equations and then use nonlinear iterative methods to iteratively solve, such as Newton’s method (Radu et al. in On the convergence of the Newton method for the mixed finite element discretization of a class of degenerate parabolic equation. Numerical mathematics and advanced applications. Springer, pp 1194–1200, 2006), Picard method (Lehmann and Ackerer 1998), and the L-method (List and Radu 2016). The Picard method can be considered as a simplified Newton method, which linearly converges.

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Accelerated double-step scale splitting iteration method for solving a class of complex symmetric linear systems

Cited by 18 publications

References 20 publications

Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations

Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations

Two lopsided TSCSP (LTSCSP) iteration methods for solution of complex symmetric positive definite linear systems

Improved Linear and Nonlinear Iterative Methods for Rainfall Infiltration Simulation

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