---
name: "damped_newton"
section: "3rheolef"
platform: "linux"
package: "librheolef-dev"
version: "7.2-4"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/damped_newton"
---

# damped\_newton(3rheolef)

nonlinear solver (rheolef-7.2)

## NAME

damped\_newton - nonlinear solver (rheolef-7.2)

## SYNOPSIS

```
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)
```

## DESCRIPTION

This function implements a generic damped Newton method for the resolution of the following problem:

```
    F(u) = 0
```

 Recall that the damped Newton method is more robust than the basic Newton one: it converges from any initial value.

A simple call to the algorithm writes:

```
    my_problem P;
    field uh (Xh);
    damped_newton (P, uh, tol, max_iter);
```

 In addition to the members required for the **newton(3)** method, two additional members are required for the damped variant:

```
    class my_problem {
    public:
      ...
      value_type derivative_trans_mult (const value_type& mrh) const;
      Float space_norm (const value_type& uh) const;
    };
```

 The `derivative_trans_mult` is used for computing the damping coefficient. The `space_norm` represents usually a L2 norm e.g. formally:

```
                          /
    space_norm(uh) = sqrt |       |uh(x)|^2 dx
                          / Omega
```

## EXAMPLE

See the **p\_laplacian\_damped\_newton.cc** example and the **usersguide** for more.

## IMPLEMENTATION

This documentation has been generated from file main/lib/damped\_newton.h

## AUTHOR

Pierre  Saramito  \<Pierre.Saramito@imag.fr\>

## 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.