Solving general sparse linear systems using conjugate gradient-type methods

1990 ◽  
Author(s):  
K. Gallivan ◽  
A. Sameh ◽  
Z. Zlatev
Keyword(s):  
Linear Systems ◽  
Conjugate Gradient ◽  
Sparse Linear Systems ◽  
Gradient Type ◽  
Conjugate Gradient Type Methods

A note on conjugate-gradient type methods for indefinite and/or inconsistent linear systems

1996 ◽  
Vol 11 (1) ◽  
pp. 181-187 ◽  
Author(s):  
Bernd Fischer ◽  
Martin Hanke ◽  
Marlis Hochbruck
Keyword(s):  
Linear Systems ◽  
Conjugate Gradient ◽  
Gradient Type ◽  
Conjugate Gradient Type Methods

GENERIC APPROXIMATE SPARSE INVERSE MATRIX TECHNIQUES

2014 ◽  
Vol 11 (06) ◽  
pp. 1350084 ◽  
Author(s):  
CHRISTOS K. FILELIS-PAPADOPOULOS ◽  
GEORGE A. GRAVVANIS
Keyword(s):  
Linear Systems ◽  
Krylov Subspace ◽  
Coefficient Matrix ◽  
Sparse Linear Systems ◽  
Approximate Inverse ◽  
Matrix Algorithm ◽  
Sparsity Pattern ◽  
Gradient Type ◽  
Comparative Results ◽  
Conjugate Gradient Type Methods

During the last decades explicit preconditioning methods have gained interest among the scientific community, due to their efficiency for solving large sparse linear systems in conjunction with Krylov subspace iterative methods. The effectiveness of explicit preconditioning schemes relies on the fact that they are close approximants to the inverse of the coefficient matrix. Herewith, we propose a Generic Approximate Sparse Inverse (GenASPI) matrix algorithm based on ILU(0) factorization. The proposed scheme applies to matrices of any structure or sparsity pattern unlike the previous dedicated implementations. The new scheme is based on the Generic Approximate Banded Inverse (GenAbI), which is a banded approximate inverse used in conjunction with Conjugate Gradient type methods for the solution of large sparse linear systems. The proposed GenASPI matrix algorithm, is based on Approximate Inverse Sparsity patterns, derived from powers of sparsified matrices and is computed with a modified procedure based on the GenAbI algorithm. Finally, applicability and implementation issues are discussed and numerical results along with comparative results are presented.

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