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.de Id
..
.de Sp
.if n .sp
.if t .sp 0.4
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.TH damped_newton 4rheolef "rheolef-6.5" "rheolef-6.5" "rheolef-6.5"
.\" label: /*Class:damped_newton
.SH NAME
\fBdamped_newton\fP -- damped Newton nonlinear algorithm
.\" skip: @findex damped\_newton
.\" skip: @cindex nonlinear problem
.\" skip: @cindex Newton method
.SH DESCRIPTION

Nonlinear damped Newton algorithm for the resolution of the following problem:
.\" begin_example
.Sp
.nf
       F(u) = 0
.Sp
.fi
.\" end_example
A simple call to the algorithm writes:
.\" begin_example
.Sp
.nf
    my_problem P;
    field uh (Vh);
    damped_newton (P, uh, tol, max_iter);
.Sp
.fi
.\" end_example
In addition to the members required for the Newton algorithm (see newton(4)),
the \fBspace_norm\fP and \fBduality_product\fP are required for
the damped Newton line search algorithm:
.\" begin_example
.Sp
.nf
    class my_problem {
    public:
      ...
      Float space_norm      (const field& uh) const;
      Float duality_product (const field& mrh, const field& msh) const;
    };
.Sp
.fi
.\" end_example
.\" skip start:AUTHOR:

.\" skip start:DATE:
.\" skip start:METHODS:
.\" END
.SH IMPLEMENTATION
.\" begin_example
.Sp
.nf
template <class Problem, class Field, class Real, class Size>
int damped_newton (Problem P, Field& u, Real& tol, Size& max_iter, odiststream* p_derr=0) {
  return damped_newton(P, newton_identity_preconditioner(), u, tol, max_iter, p_derr);
}
.Sp
.fi
.\" end_example

.\" LENGTH = 1
.SH SEE ALSO
newton(4)