Block SOR two-stage iterative methods for solution of symmetric positive definite linear systems

Cai, Fang; Xiao, Jie; Zhao-hong, Xiang

doi:10.1109/icacte.2010.5578996

Cited by 4 publications

(2 citation statements)

References 11 publications

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“…The two-stage method was first introduced in 1973 by Nichols [21] and has received wide attention throughout the years. The literature includes convergence criteria and comparison theorems for a variety of coefficients matrices: M-matrices [23], H-matrices [24], Hermitian positive definite [9,[25][26][27] and semidefinite [28]. Within each class, different conditions on the splittings have been studied, such as (weak-)regular [23] and P-regular splittings [9].…”

Section: Nested Matrix Splittingsmentioning

confidence: 99%

Parallelization of Hermitian positive definite systems of equations: A hierarchical Jacobi approach

Inghelbrecht

Barbé

2022

Linear Algebra and its Applications

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Section: Nested Matrix Splittingsmentioning

confidence: 99%

Parallelization of Hermitian positive definite systems of equations: A hierarchical Jacobi approach

Inghelbrecht

Barbé

2022

Linear Algebra and its Applications

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“…In this paper, several stationary iterative methods are reviewed, i.e., Alternating Group Explicit [10], Modified Alternating Group Explicit [11], Iterative Alternating Decomposition Explicit [12], Block SOR [13], and Weighted Mean (WM) [14,15]. Among these names of stationary iterative method, the concept from the WM method is adopted to develop a new efficient numerical method for porous medium type equation.…”

Section: Preliminarymentioning

confidence: 99%

A Newton-Modified Weighted Arithmetic Mean Solution of Nonlinear Porous Medium Type Equations

et al. 2021

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The mathematical theory behind the porous medium type equation is well developed and produces many applications to the real world. The research and development of the fractional nonlinear porous medium models also progressed significantly in recent years. An efficient numerical method to solve porous medium models needs to be investigated so that the symmetry of the designed method can be extended to future fractional porous medium models. This paper contributes a new numerical method called Newton-Modified Weighted Arithmetic Mean (Newton-MOWAM). The solution of the porous medium type equation is approximated by using a finite difference method. Then, the Newton method is applied as a linearization approach to solving the system of nonlinear equations. As the system to be solved is large, high computational complexity is regulated by the MOWAM iterative method. Newton-MOWAM is formulated technically based on the matrix structure of the system. Some initial-boundary value problems with a different type of nonlinear diffusion term are presented. As a result, the Newton-MOWAM showed a significant improvement in the computation efficiency compared to the developed standard Weighted Arithmetic Mean iterative method. The analysis of efficiency, measured by the reduced number of iterations and computation time, is reported along with the convergence analysis.

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A New Variant of Arithmetic Mean Iterative Method for Fourth Order Integro-differential Equations Solution

Aruchunan

Wiwatanapataphee

et al. 2015

2015 3rd International Conference on Artificial Intelligence, Modelling and Simulation (AIMS)

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Block SOR two-stage iterative methods for solution of symmetric positive definite linear systems

Cited by 4 publications

References 11 publications

Parallelization of Hermitian positive definite systems of equations: A hierarchical Jacobi approach

Parallelization of Hermitian positive definite systems of equations: A hierarchical Jacobi approach

A Newton-Modified Weighted Arithmetic Mean Solution of Nonlinear Porous Medium Type Equations

A New Variant of Arithmetic Mean Iterative Method for Fourth Order Integro-differential Equations Solution

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