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.TH damped_newton 4rheolef "rheolef-7.0" "rheolef-7.0" "rheolef-7.0"
.\" 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 is required for the damped Newton line search algorithm:
.\" begin_example
.Sp
.nf
    class my_problem {
    public:
      ...
      value_type derivative_trans_mult (const value_type& mrh) const;
      Float space_norm (const value_type& uh) 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 (const Problem& F, Field& u, Real& tol, Size& max_iter, odiststream* p_derr=0)
.Sp
.fi
.\" end_example

.\" LENGTH = 1
.SH SEE ALSO
newton(4)
.SH COPYRIGHT
Copyright (C) 2000-2018 Pierre Saramito <Pierre.Saramito@imag.fr> GPLv3+: GNU GPL version 3 or later <http://gnu.org/licenses/gpl.html>.
This is free software: you are free to change and redistribute it.  There is NO WARRANTY, to the extent permitted by law.