Chapter 5: Matrix Splitting Iteration Methods

2021 ◽  
pp. 171-242
Keyword(s):  
Matrix Splitting ◽  
Iteration Methods

scholarly journals The modified matrix splitting iteration method for computing PageRank problem

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 725-740 ◽  
Author(s):  
Zhaolu Tian ◽  
Xiaoyan Liu ◽  
Yudong Wang ◽  
P.H. Wen
Keyword(s):  
Iteration Method ◽  
Matrix Splitting ◽  
Power Method ◽  
Numerical Examples ◽  
Comparison Results ◽  
Iteration Methods ◽  
Splitting Iteration Method ◽  
Outer Iteration

In this paper, based on the iteration methods [3,10], we propose a modified multi-step power-inner-outer (MMPIO) iteration method for solving the PageRank problem. In the MMPIO iteration method, we use the multi-step matrix splitting iterations instead of the power method, and combine with the inner-outer iteration [24]. The convergence of the MMPIO iteration method is analyzed in detail, and some comparison results are also given. Several numerical examples are presented to illustrate the effectiveness of the proposed algorithm.

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