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See the recommended documentation of this function
gmres
Generalized Minimum RESidual method
Calling Sequence
[x,flag,err,iter,res] = gmres(A,b,rstr,tol,maxi,M,x0)
Arguments
- A
n-by-n matrix or function returning
A*x
- b
right hand side vector
- x0
initial guess vector (default: zeros(n,1))
- M
preconditioner: matrix or function returning
M*x
(In the first case, default: eye(n,n))- rstr
number of iterations between restarts (default: 10)
- maxi
maximum number of iterations (default: n)
- tol
error tolerance (default: 1e-6)
- x
solution vector
- err
final residual norm
- iter
number of iterations performed
- flag
- 0 =
gmres
converged to the desired tolerance withinmaxi
iterations- 1 =
no convergence given
maxi
- res
residual vector
Description
- GMRES
solves the linear system
Ax=b
using the Generalized Minimal residual method with restarts.- Details
of this algorithm are described in :
"Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra, Eijkhout, Pozo, Romine, and Van der Vorst, SIAM Publications, 1993 (ftp netlib2.cs.utk.edu; cd linalg; get templates.ps).
"Iterative Methods for Sparse Linear Systems, Second Edition" Saad, SIAM Publications, 2003 (ftp ftp.cs.umn.edu; cd dept/users/saad/PS; get all_ps.zip).
Examples
// GMRES call x=gmres(A,b);
See Also
Authors
Sage Group (IRISA, 2005)
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