scholarly journals A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method

1996 ◽  
Vol 17 (5) ◽  
pp. 1135-1149 ◽  
Author(s):  
Michele Benzi ◽  
Carl D. Meyer ◽  
Miroslav Tůma
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Approximate Inverse ◽  
Sparse Approximate Inverse

A Class of Symmetric Factored Approximate Inverses and Hybrid Two-Level Solver

2018 ◽  
Vol 15 (06) ◽  
pp. 1850050 ◽  
Author(s):  
Panagiotis E. Kyziropoulos ◽  
Christos K. Filelis-Papadopoulos ◽  
George A. Gravvanis
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Independent Set ◽  
Schur Complement ◽  
Preconditioned Conjugate Gradient Method ◽  
Preconditioned Conjugate Gradient ◽  
Approximate Inverse ◽  
New Class ◽  
Approximate Inverses

A new class of symmetric factored approximate inverses is proposed and used in conjunction with the Preconditioned Conjugate Gradient method for solving sparse symmetric linear systems. Additionally, a new hybrid two-level solver is proposed utilizing a block independent set reordering, in order to create the two level hierarchy. The Schur complement is formed explicitly by inverting the blocks created by reordering. Then, the preconditioned conjugate gradient method is used in conjunction with the symmetric factored approximate inverse to solve the reduced order linear system. Furthermore, numerical results on the performance and convergence behavior for solving various model problems are presented.

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