Alternating Lower-Upper Splitting Iterative Method for Positive Definite Linear Systems

2011 ◽  
pp. 63-66
Keyword(s):  
Iterative Method ◽  
Linear Systems ◽  
Positive Definite ◽  
Lower Upper

scholarly journals Convergence of TTS Iterative Method for Non-Hermitian Positive Definite Linear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Cheng-Yi Zhang ◽  
Yu-Qian Yang ◽  
Qiang Sun
Keyword(s):  
Iterative Method ◽  
Linear Systems ◽  
Positive Definite ◽  
Convergence Theorems ◽  
Convergence Conditions

The TTS iterative method is proposed to solve non-Hermitian positive definite linear systems and some convergence conditions are presented. Subsequently, these convergence conditions are applied to the ALUS method proposed by Xiang et al. in 2012 and comparison of some convergence theorems is made. Furthermore, an example is given to demonstrate the results obtained in this paper.

Study of an Iterative Solution for Boltzmann Transport Equation and Calculation of Thermal Conductivity

2018 ◽  
Vol 777 ◽  
pp. 421-425 ◽  
Author(s):  
Chhengrot Sion ◽  
Chung Hao Hsu
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Numerical Calculation ◽  
Iterative Method ◽  
Transport Equation ◽  
Linear Systems ◽  
Heat Transport ◽  
Boltzmann Transport Equation ◽  
Iterative Solution ◽  
Boltzmann Transport

Many methods have been developed to predict the thermal conductivity of the material. Heat transport is complex and it contains many unknown variables, which makes the thermal conductivity hard to define. The iterative solution of Boltzmann transport equation (BTE) can make the numerical calculation and the nanoscale study of heat transfer possible. Here, we review how to apply the iterative method to solve BTE and many linear systems. This method can compute a sequence of progressively accurate iteration to approximate the solution of BTE.

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