scholarly journals Toward efficient polynomial preconditioning for GMRES

2021 ◽  
Author(s):  
Jennifer A. Loe ◽  
Ronald B. Morgan
Keyword(s):  
Polynomial Preconditioning

Adaptive polynomial preconditioning for hermitian indefinite linear systems

1989 ◽  
Vol 29 (4) ◽  
pp. 583-609 ◽  
Author(s):  
Steven F. Ashby ◽  
Thomas A. Manteuffel ◽  
Paul E. Saylor
Keyword(s):  
Linear Systems ◽  
Polynomial Preconditioning ◽  
Indefinite Linear Systems

Polynomial preconditioning in Krylov-ROW-methods

1998 ◽  
Vol 28 (2-4) ◽  
pp. 427-437 ◽  
Author(s):  
Bernhard A. Schmitt ◽  
Rüdiger Weiner
Keyword(s):  
Polynomial Preconditioning

A Preconditioned Minimal Residual Solver for a Class of Linear Operator Equations

2010 ◽  
Vol 10 (2) ◽  
pp. 119-136
Author(s):  
O. Awono ◽  
J. Tagoudjeu
Keyword(s):  
Linear Operator ◽  
Neutron Transport ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Operator Equations ◽  
Infinite Dimensional ◽  
Polynomial Preconditioning ◽  
Residual Algorithm ◽  
Linear Operator Equations ◽  
Minimal Residual

Abstract We consider the class of linear operator equations with operators admitting self-adjoint positive definite and m-accretive splitting (SAS). This splitting leads to an ADI-like iterative method which is equivalent to a fixed point problem where the operator is a 2 by 2 matrix of operators. An infinite dimensional adaptation of a minimal residual algorithm with Symmetric Gauss-Seidel and polynomial preconditioning is then applied to solve the resulting matrix operator equation. Theoretical analysis shows the convergence of the methods, and upper bounds for the decrease rate of the residual are derived. The convergence of the methods is numerically illustrated with the example of the neutron transport problem in 2-D geometry.

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