gmres

Scilab Function
Last update : 06/01/2006

gmres - generalized minimum residual method with restarts

### Calling Sequence

  `[x,flag,err,iter,res] = gmres(A,b,rstr,tol,maxi,M,x0)`

### Parameters

- `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 within `maxi` iterations
- `res` : residual vector

### Description

Solves the linear system `Ax=b` using the Generalized Minimal residual (GMRES(m)) method with restarts.

### See Also

`pcg`,

### Author

Sage Group (IRISA, 2005)