A Correction Concerning the Convergence Rate for the Conjugate Gradient Method

1970 ◽  
Vol 7 (2) ◽  
pp. 277-280 ◽  
Author(s):  
James W. Daniel
Keyword(s):  
Convergence Rate ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method

Restricted Additive Schwarz Preconditioner for Elliptic Equations with Jump Coefficients

2016 ◽  
Vol 8 (6) ◽  
pp. 1072-1083 ◽  
Author(s):  
Zhiyong Liu ◽  
Yinnian He
Keyword(s):  
Convergence Rate ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Elliptic Equations ◽  
Preconditioned Conjugate Gradient ◽  
Additive Schwarz ◽  
Large Jump ◽  
Second Order Elliptic Problems ◽  
Schwarz Preconditioner

AbstractThis paper provides a proof of robustness of the restricted additive Schwarz preconditioner with harmonic overlap (RASHO) for the second order elliptic problems with jump coefficients. By analyzing the eigenvalue distribution of the RASHO preconditioner, we prove that the convergence rate of preconditioned conjugate gradient method with RASHO preconditioner is uniform with respect to the large jump and meshsize.

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