Newton method generalized to any dimension N: Solves the system G(X) = 0, where G is a regular but non-linear application \( R^N \rightarrow R^N \) . More...

Public Member Functions
	NewtonMD (int N=1, LinAlgUtils::Method linMethod=LinAlgUtils::ColQR)

virtual	~NewtonMD ()

int	getN () const

void	setN (int n)

LinAlgUtils::Method	getLinMethod () const

void	setLinMethod (LinAlgUtils::Method linMethod)

template<class OBJ , typename FUNC , typename JACOB >
VectorD	solve (OBJ *object, FUNC G, const std::vector< double > &funcParameters, VectorD X0, JACOB J_G=0, const double absTolerance=1.e-4, const double relTolerance=1.e-4, const size_t maxIteration=50)

VectorD	iterate (const VectorD &X0, const VectorD &G_X0, const MatrixD &J_G_X0)
	Produces a new iteration by solving the linear system J^G(X0) * (X0 - X1) = G(X0) and returns X1. More...

Private Attributes
int	m_N
	Dimension of the problem. More...

LinAlgUtils::Method	m_linMethod
	Method used for solving linear systems. More...

Detailed Description

Newton method generalized to any dimension N: Solves the system G(X) = 0, where G is a regular but non-linear application \( R^N \rightarrow R^N \) .

The class can be used either through templates with the solve method providing G and the Jacobian matrix functions pointers, or manually through instantiating an object NewtonMD and iterating the method iterate by giving G(X) and the Jacobian matrix at each step, to avoid using functions.

For linear G (matrices), use the LinearSystem class.

Constructor & Destructor Documentation

◆ NewtonMD()

NumA::NewtonMD::NewtonMD	(	int	N = `1`,
		LinAlgUtils::Method	linMethod = `LinAlgUtils::ColQR`
	)

◆ ~NewtonMD()

NumA::NewtonMD::~NewtonMD ( )

virtual

Member Function Documentation

◆ getLinMethod()

LinAlgUtils::Method NumA::NewtonMD::getLinMethod ( ) const

◆ getN()

int NumA::NewtonMD::getN ( ) const

◆ iterate()

VectorD NumA::NewtonMD::iterate	(	const VectorD &	X0,
		const VectorD &	G_X0,
		const MatrixD &	J_G_X0
	)

Produces a new iteration by solving the linear system J^G(X0) * (X0 - X1) = G(X0) and returns X1.

Parameters

X0	: VectorD of size N
G_X0	: VectorD of size N
J_G_X0	: MatrixD of size NxN

Returns: X1 : New solution after the new iteration.

◆ setLinMethod()

void NumA::NewtonMD::setLinMethod ( LinAlgUtils::Method linMethod )

◆ setN()

void NumA::NewtonMD::setN ( int n )

◆ solve()

template<class OBJ , typename FUNC , typename JACOB >

VectorD NumA::NewtonMD::solve	(	OBJ *	object,
		FUNC	G,
		const std::vector< double > &	funcParameters,
		VectorD	X0,
		JACOB	J_G = `0`,
		const double	absTolerance = `1.e-4`,
		const double	relTolerance = `1.e-4`,
		const size_t	maxIteration = `50`
	)

inline

Member Data Documentation

◆ m_linMethod

LinAlgUtils::Method NumA::NewtonMD::m_linMethod

private

Method used for solving linear systems.

◆ m_N

int NumA::NewtonMD::m_N