The convergence conditions of the psd iterative method for linear systems

2001 ◽  
Vol 77 (4) ◽  
pp. 569-581
Author(s):  
Da-Wei Chang
Keyword(s):  
Iterative Method ◽  
Linear Systems ◽  
Convergence Conditions

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.

scholarly journals A Modification of Minimal Residual Iterative Method to Solve Linear Systems

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Xingping Sheng ◽  
Youfeng Su ◽  
Guoliang Chen
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Linear Systems ◽  
Residual Error ◽  
Projection Technique ◽  
Numerical Example ◽  
Minimal Residual

We give a modification of minimal residual iteration (MR), which is 1V-DSMR to solve the linear systemAx=b. By analyzing, we find the modifiable iteration to be a projection technique; moreover, the modification of which gives a better (at least the same) reduction of the residual error than MR. In the end, a numerical example is given to demonstrate the reduction of the residual error between the 1V-DSMR and MR.

Approximate Solution of Linear Systems with Laplace-like Operators via Cross Approximation in the Frequency Domain

2019 ◽  
Vol 19 (1) ◽  
pp. 137-145 ◽  
Author(s):  
Ekaterina A. Muravleva ◽  
Ivan V. Oseledets
Keyword(s):  
Approximate Solution ◽  
Iterative Method ◽  
Frequency Domain ◽  
Linear Systems ◽  
Stokes Problem ◽  
Inverse Operator ◽  
Low Rank ◽  
Low Rank Approximation ◽  
Rank Approximation ◽  
Reduced Complexity

AbstractIn this paper we propose an efficient algorithm to compute low-rank approximation to the solution of so-called “Laplace-like” linear systems. The idea is to transform the problem into the frequency domain, and then use cross approximation. In this case, we do not need to form explicit approximation to the inverse operator, and can approximate the solution directly, which leads to reduced complexity. We demonstrate that our method is fast and robust by using it as a solver inside Uzawa iterative method for solving the Stokes problem.

scholarly journals An Iterative Method Using Piecewise Valued Basic Vectors for Solving Linear Systems with Symmetric Coefficient Matrix

2004 ◽  
Vol 7 ◽  
pp. 247-254
Author(s):  
Takuro KATAYAMA ◽  
Mitsuhiro KASHIWAGI ◽  
Shin-ichi OHWAKI ◽  
Toshitaka YAMAO
Keyword(s):  
Iterative Method ◽  
Linear Systems ◽  
Coefficient Matrix
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