.TH "damped_newton" 3rheolef "Version 7.2" "rheolef" \" -*- nroff -*-
.ad l
.nh
.SH NAME
damped_newton \- nonlinear solver (rheolef-7\&.2)
.PP
 
.SH "SYNOPSIS"
.PP
.PP
.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)
.fi
.PP
.SH "DESCRIPTION"
.PP
This function implements a generic damped Newton method for the resolution of the following problem: 
.PP
.nf
    F(u) = 0

.fi
.PP
 Recall that the damped Newton method is more robust than the basic Newton one: it converges from any initial value\&.
.PP
A simple call to the algorithm writes: 
.PP
.nf
    my_problem P;
    field uh (Xh);
    damped_newton (P, uh, tol, max_iter);

.fi
.PP
 In addition to the members required for the \fBnewton(3)\fP method, two additional members are required for the damped variant: 
.PP
.nf
    class my_problem {
    public:
      \&.\&.\&.
      value_type derivative_trans_mult (const value_type& mrh) const;
      Float space_norm (const value_type& uh) const;
    };

.fi
.PP
 The \fCderivative_trans_mult\fP is used for computing the damping coefficient\&. The \fCspace_norm\fP represents usually a L2 norm e\&.g\&. formally: 
.PP
.nf
                          /
    space_norm(uh) = sqrt |       |uh(x)|^2 dx
                          / Omega

.fi
.PP
 
.SH "EXAMPLE"
.PP
See the \fBp_laplacian_damped_newton\&.cc\fP example and the \fBusersguide\fP for more\&.
.SH "IMPLEMENTATION"
.PP
This documentation has been generated from file main/lib/damped_newton\&.h 
.SH AUTHOR
Pierre  Saramito  <Pierre.Saramito@imag.fr>
.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.