newton.h File Reference

#include "../utils.h"
#include "gaussSeidel.h"
#include <functional>

Go to the source code of this file.

Typedefs
using	Jacobian = std::function< Matrix< double >(const Matrix< double > &)>
	representation of jacobian More...
using	LinearEquation = std::function< Matrix< double >(const Matrix< double > &)>
	representation of linear equation More...

Functions
std::pair< Matrix< double >, int >	newton (const LinearEquation &f, const Jacobian &Df, const Matrix< double > &x0, double TOL, int maxIter)

Detailed Description

Implements newton-method to find roots

Requires:

#include <math/numerics/lin_alg/newton.h>

Typedef Documentation

Jacobian

using Jacobian = std::function<Matrix<double>(const Matrix<double>&)>

representation of jacobian

LinearEquation

using LinearEquation = std::function<Matrix<double>(const Matrix<double>&)>

representation of linear equation

Function Documentation

newton()

std::pair< Matrix< double >, int > newton	(	const LinearEquation &	f,
		const Jacobian &	Df,
		const Matrix< double > &	x0,
		double	TOL,
		int	maxIter
	)

newton method to find roots of given function f

Parameters

f	linear equation
Df	derivative of f
x0	start value
TOL	desired tolerance of the method
maxIter	maximum iterations for the method

Returns

approximated values paired with required number iterations for given tolerance

Examples

numerics/lin_alg/TestNewton.cpp.