qmr

Scilab Function
Last update : 14/09/2005

qmr - quasi minimal resiqual method with preconditioning

### Calling Sequence

  `[x,flag,err,iter,res] = qmr(A,b,x0,M1,M1p,M2,M2p,maxi,tol)`

### Parameters

- `A` : matrix of size n-by-n or function returning `A*x`
- `b` : right hand side vector
- `x0` : initial guess vector (default: zeros(n,1))
- `M1` : left preconditioner: matrix or function returning `M1*x` (In the first case, default: eye(n,n))
- `M1p` : must only be provided when `M1` is a function. In this case `M1p` is the function which returns `M1'*x`
- `M2` : right preconditioner: matrix or function returning `M2*x` (In the first case, default: eye(n,n))
- `M2p` : must only be provided when `M2` is a function. In this case `M2p` is the function which returns `M2'*x`
- `maxi` : maximum number of iterations (default: n)
- `tol` : error tolerance (default: 1000*%eps)
- `x` : solution vector
- `flag` : 0 = `qmr` converged to the desired tolerance within `maxi` iterations
- `res` : residual vector
- `err` : final residual norm
- `iter` : number of iterations performed

### Description

Solves the linear system `Ax=b` using the Quasi Minimal Residual Method with preconditioning.

### See Also

`gmres` ,

### Author

SAGE Group, IRISA 2005