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## man page of qmr

### qmr: quasi-minimal residual algoritm

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## NAME

qmr- quasi-minimal residual algoritm## SYNOPSIS

template <class Matrix, class Vector, class Preconditioner1, class Preconditioner2, class Real> int qmr (const Matrix &A, Vector &x, const Vector &b, const Preconditioner1 &M1, const Preconditioner2 &M2, int &max_iter, Real &tol);EXAMPLE

The simplest call to 'qmr' has the folling form: int status = qmr(a, x, b, EYE, EYE, 100, 1e-7);## DESCRIPTION

qmrsolves the unsymmetric linear system Ax = b using the the quasi- minimal residual method. The return value indicates convergence within max_iter (input) iterations (0), or no convergence within max_iter iterations (1). Upon successful return, output arguments have the following values:xapproximate solution to Ax = bmax_iterthe number of iterations performed before the tolerance was reachedtolthe residual after the final iteration A return value of 1 indicates that the method did not reach the specified convergence tolerance in the maximum numbefr of iterations. A return value of 2 indicates that a breackdown associated withrhooccurred. A return value of 3 indicates that a breackdown associated withbetaoccurred. A return value of 4 indicates that a breackdown associated withgammaoccurred. A return value of 5 indicates that a breackdown associated withdeltaoccurred. A return value of 6 indicates that a breackdown associated withepsilonoccurred. A return value of 7 indicates that a breackdown associated withxioccurred.## NOTE

qmr is an iterative template routine. qmr follows the algorithm described on p. 24 in @quotation Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd Edition, R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. Van der Vorst, SIAM, 1994, ftp.netlib.org/templates/templates.ps. @end quotation The present implementation is inspired from IML++ 1.2 iterative method library, //math.nist.gov/iml++. QMR(5)

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