---
name: "damped-newton"
section: "4rheolef"
platform: "linux"
package: "librheolef-dev"
version: "6.1-2.1"
release: "Debian 7 (Wheezy)"
platforms: ["linux"]
url: "https://new.carta.tech/damped-newton"
---

# damped-newton(4rheolef)

## NAME

**damped\_newton** -- damped Newton nonlinear algorithm

## DESCRIPTION

Nonlinear damped Newton algorithm for the resolution of the following problem:

```
       F(u) = 0

```

A simple call to the algorithm writes:

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

```

The **my\_problem** class may contains methods for the evaluation of F (aka residue) and its derivative:

```
    class my_problem {
    public:
      my_problem();
      field residue (const field& uh) const;
      void update_derivative (const field& uh) const;
      field derivative_trans_mult (const field& mrh) const;
      field derivative_solve (const field& mrh) const;
      Float norm (const field& uh) const;
      Float dual_norm (const field& Muh) const;
    };

```

See the example **p-laplacian.h** in the user's documentation for more.

## IMPLEMENTATION

```
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);
}

```