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# qmr

quasi minimal resiqual method with preconditioning

### Calling Sequence

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

### Arguments

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 =

`gmres` converged to the desired tolerance within `maxi` iterations

1 =

no convergence given `maxi`

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.

• gmres — Generalized Minimum RESidual method

### Authors

SAGE Group, IRISA 2005

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